IdStatementProofNames
0→𝜑→𝜓𝜑Axiomax-1
1→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒Axiomax-2
2→→¬𝜑¬𝜓→𝜓𝜑Axiomax-3, con4
3¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Axiomdf-bi
4↔⋀𝜑𝜓¬→𝜑¬𝜓Axiomdf-an
5→𝜑→𝜑𝜑Subs [𝜓↗𝜑] into ax-1
6→𝜑→→𝜑𝜑𝜑Subs [𝜓↗→𝜑𝜑] into ax-1
7→→𝜑→→𝜑𝜑𝜑→→𝜑→𝜑𝜑→𝜑𝜑Subs [𝜓↗→𝜑𝜑, 𝜒↗𝜑] into ax-2
8→→𝜑→𝜑𝜑→𝜑𝜑Modus ponens 6, 7
9→𝜑𝜑Modus ponens 5, 8id
10→𝜓𝜓Subs [𝜑↗𝜓] into id
11→→𝜓𝜓→𝜑→𝜓𝜓Subs [𝜑↗→𝜓𝜓, 𝜓↗𝜑] into ax-1
12→𝜑→𝜓𝜓Modus ponens 10, 11idd
13→𝜑→𝜒𝜑Subs [𝜓↗𝜒] into ax-1
14→→𝜑→𝜒𝜑→𝜑→𝜑→𝜒𝜑Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗𝜑] into ax-1
15→𝜑→𝜑→𝜒𝜑Modus ponens 13, 14
16→→𝜑→𝜑→𝜒𝜑→→𝜑𝜑→𝜑→𝜒𝜑Subs [𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2
17→→𝜑𝜑→𝜑→𝜒𝜑Modus ponens 15, 16
18→→𝜒𝜑→𝜓→𝜒𝜑Subs [𝜑↗→𝜒𝜑] into ax-1
19→→→𝜒𝜑→𝜓→𝜒𝜑→𝜑→→𝜒𝜑→𝜓→𝜒𝜑Subs [𝜑↗→→𝜒𝜑→𝜓→𝜒𝜑, 𝜓↗𝜑] into ax-1
20→𝜑→→𝜒𝜑→𝜓→𝜒𝜑Modus ponens 18, 19
21→→𝜑→→𝜒𝜑→𝜓→𝜒𝜑→→𝜑→𝜒𝜑→𝜑→𝜓→𝜒𝜑Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜓→𝜒𝜑] into ax-2
22→→𝜑→𝜒𝜑→𝜑→𝜓→𝜒𝜑Modus ponens 20, 21
23→𝜑→𝜓→𝜒𝜑Modus ponens 13, 222a1
24→→𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓] into id
25→𝜑→→𝜑𝜓𝜑Subs [𝜓↗→𝜑𝜓] into ax-1
26→→𝜑→→𝜑𝜓𝜑→𝜑→𝜑→→𝜑𝜓𝜑Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1
27→𝜑→𝜑→→𝜑𝜓𝜑Modus ponens 25, 26
28→→𝜑→𝜑→→𝜑𝜓𝜑→→𝜑𝜑→𝜑→→𝜑𝜓𝜑Subs [𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2
29→→𝜑𝜑→𝜑→→𝜑𝜓𝜑Modus ponens 27, 28
30→→→𝜑𝜓→𝜑𝜓→→→𝜑𝜓𝜑→→𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
31→→→𝜑𝜓𝜑→→𝜑𝜓𝜓Modus ponens 24, 30
32→→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
33→𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓Modus ponens 31, 32
34→→𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜑→𝜑→→𝜑𝜓𝜓Subs [𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2
35→→𝜑→→𝜑𝜓𝜑→𝜑→→𝜑𝜓𝜓Modus ponens 33, 34
36→𝜑→→𝜑𝜓𝜓Modus ponens 25, 35pm2.27
37→→𝜑→→𝜑𝜓𝜓→→𝜑→𝜑𝜓→𝜑𝜓Subs [𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2
38→→𝜑→𝜑𝜓→𝜑𝜓Modus ponens pm2.27, 37pm2.43
39→→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into ax-1
40→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
41→→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 39, 40
42→→→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2
43→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 41, 42
44→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
45→→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓→→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓Subs [𝜑↗→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
46→→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓Modus ponens 44, 45
47→→→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒𝜑→𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→→𝜒𝜑→𝜒𝜓] into ax-2
48→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒𝜑→𝜒𝜓Modus ponens 46, 47
49→→𝜑𝜓→→𝜒𝜑→𝜒𝜓Modus ponens 39, 48imim2
50→→𝜑𝜓→𝜒𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into idd
51→→𝜒𝜒→𝜓→𝜒𝜒Subs [𝜑↗→𝜒𝜒] into ax-1
52→→→𝜒𝜒→𝜓→𝜒𝜒→→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗→𝜑𝜓] into ax-1
53→→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒Modus ponens 51, 52
54→→→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜓→𝜒𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2
55→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜓→𝜒𝜒Modus ponens 53, 54
56→→𝜑𝜓→𝜓→𝜒𝜒Modus ponens 50, 55
57→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into ax-2
58→→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
59→→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Modus ponens 57, 58
60→→→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→→𝜑𝜓→𝜓→𝜒𝜒→→𝜑𝜓→→𝜓𝜒→𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2
61→→→𝜑𝜓→𝜓→𝜒𝜒→→𝜑𝜓→→𝜓𝜒→𝜓𝜒Modus ponens 59, 60
62→→𝜑𝜓→→𝜓𝜒→𝜓𝜒Modus ponens 56, 61
63→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-1
64→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
65→→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens 63, 64
66→→→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2
67→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens 65, 66
68→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imim2
69→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1
70→→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 68, 69
71→→→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
72→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 70, 71
73→→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
74→→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 72, 73
75→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2
76→→→𝜑𝜓→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 74, 75
77→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 62, 76
78→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
79→→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
80→→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 78, 79
81→→→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2
82→→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 80, 81
83→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 77, 82
84→→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2
85→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 83, 84
86→→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 63, 85imim1
87→→𝜓𝜒→→𝜒𝜃→𝜓𝜃Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into imim1
88→→→𝜓𝜒→→𝜒𝜃→𝜓𝜃→𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃Subs [𝜑↗→→𝜓𝜒→→𝜒𝜃→𝜓𝜃, 𝜓↗𝜑] into ax-1
89→𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃Modus ponens 87, 88
90→→𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃Subs [𝜓↗→𝜓𝜒, 𝜒↗→→𝜒𝜃→𝜓𝜃] into ax-2
91→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃Modus ponens 89, 90
92→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃Subs [𝜓↗→𝜒𝜃, 𝜒↗→𝜓𝜃] into ax-2
93→→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃Subs [𝜑↗→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃, 𝜓↗→𝜑→𝜓𝜒] into ax-1
94→→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃Modus ponens 92, 93
95→→→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃→→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→→𝜒𝜃→𝜓𝜃, 𝜒↗→→𝜑→𝜒𝜃→𝜑→𝜓𝜃] into ax-2
96→→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃Modus ponens 94, 95
97→→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃Modus ponens 91, 96pm2.83
98→→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imim1
99→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→→𝜑𝜓𝜑𝜑] into id
100→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
101→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑Modus ponens 99, 100
102→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑Subs [𝜑↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1
103→→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑Subs [𝜑↗→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
104→→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑Modus ponens 102, 103
105→→→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑] into ax-2
106→→→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑Modus ponens 104, 105
107→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑Modus ponens 98, 106
108→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into imim2
109→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1
110→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Modus ponens 108, 109
111→→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑] into ax-2
112→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Modus ponens 110, 111
113→→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
114→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Modus ponens 112, 113
115→→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑] into ax-2
116→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Modus ponens 114, 115
117→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑Modus ponens 101, 116
118→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→𝜒𝜑𝜑] into ax-2
119→→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
120→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Modus ponens 118, 119
121→→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜒↗→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑] into ax-2
122→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Modus ponens 120, 121
123→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Modus ponens 117, 122
124→→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑] into ax-2
125→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Modus ponens 123, 124
126→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑Modus ponens 107, 125
127→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
128→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1
129→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑Modus ponens 127, 128
130→→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑] into ax-2
131→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑Modus ponens 129, 130
132→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→𝜒𝜑𝜑] into ax-2
133→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑Modus ponens 126, 132
134→→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑Subs [𝜑↗→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1
135→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑Modus ponens 133, 134
136→→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜑𝜓𝜒→→𝜒𝜑𝜑] into ax-2
137→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑Modus ponens 135, 136
138→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑Modus ponens 127, 137peirceroll
139→→𝜑→𝜓𝜒→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒] into id
140→𝜓→→𝜓𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm2.27
141→→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒Subs [𝜑↗→𝜓→→𝜓𝜒𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
142→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒Modus ponens 140, 141
143→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒] into ax-1
144→→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
145→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒Modus ponens 143, 144
146→→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜓→𝜑→𝜓𝜒] into ax-2
147→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒Modus ponens 145, 146
148→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗𝜒, 𝜒↗𝜑] into imim2
149→→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1
150→𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 148, 149
151→→𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜓𝜒𝜒, 𝜒↗→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2
152→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 150, 151
153→→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
154→→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 152, 153
155→→→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→→𝜓𝜒𝜒, 𝜒↗→𝜓→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2
156→→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 154, 155
157→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 142, 156
158→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
159→→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒Subs [𝜑↗→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
160→→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒Modus ponens 158, 159
161→→→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒] into ax-2
162→→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒Modus ponens 160, 161
163→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒Modus ponens 157, 162
164→→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→𝜑→𝜓𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2
165→→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑𝜒Modus ponens 163, 164
166→→𝜑→𝜓𝜒→𝜓→𝜑𝜒Modus ponens 143, 165pm2.04
167→→𝜒𝜃→→𝜓𝜒→𝜓𝜃Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into imim2
168→→𝜑𝜓→→𝜓𝜃→𝜑𝜃Subs [𝜒↗𝜃] into imim1
169→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃Subs [𝜑↗→→𝜑𝜓→→𝜓𝜃→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1
170→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃Modus ponens 168, 169
171→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃Subs [𝜑↗→→𝜓𝜒→𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
172→→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃Subs [𝜑↗→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃, 𝜓↗→𝜒𝜃] into ax-1
173→→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃Modus ponens 171, 172
174→→→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→→𝜒𝜃→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜑𝜓→→𝜓𝜒→𝜓𝜃] into ax-2
175→→→𝜒𝜃→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃Modus ponens 173, 174
176→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃Modus ponens 167, 175
177→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→𝜓𝜃, 𝜓↗→𝜑𝜃, 𝜒↗→𝜓𝜒] into imim2
178→→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜑𝜓] into ax-1
179→→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 177, 178
180→→→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜃→𝜑𝜃, 𝜒↗→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃] into ax-2
181→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 179, 180
182→→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1
183→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 181, 182
184→→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→𝜓𝜃→𝜑𝜃, 𝜒↗→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃] into ax-2
185→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 183, 184
186→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 170, 185
187→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜓𝜒→𝜑𝜃] into ax-2
188→→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1
189→→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Modus ponens 187, 188
190→→→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜒↗→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃] into ax-2
191→→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Modus ponens 189, 190
192→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Modus ponens 186, 191
193→→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜃] into ax-2
194→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Modus ponens 192, 193
195→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃Modus ponens 176, 194
196→→𝜑𝜓→→𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into ax-1
197→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
198→→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓Modus ponens 196, 197
199→→→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜒𝜃→𝜑𝜓] into ax-2
200→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓Modus ponens 198, 199
201→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜃] into ax-2
202→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 195, 201
203→→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜑𝜓] into ax-1
204→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 202, 203
205→→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→→𝜓𝜒→𝜑𝜃] into ax-2
206→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 204, 205
207→→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃Modus ponens 196, 206imim12
208→𝜓→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-1
209→𝜒𝜒Subs [𝜑↗𝜒] into id
210→→𝜒𝜒→→𝜑𝜓→𝜒𝜒Subs [𝜑↗→𝜒𝜒, 𝜓↗→𝜑𝜓] into ax-1
211→→→𝜑𝜓→𝜒𝜒→→→𝜑𝜓𝜒→→𝜑𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into ax-2
212→→→𝜑𝜓𝜒→→𝜑𝜓𝜒Modus ponens 50, 211
213→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜒] into ax-1
214→→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓] into ax-1
215→𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓Modus ponens 213, 214
216→→𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒→𝜑𝜓] into ax-2
217→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓𝜒→𝜑𝜓Modus ponens 215, 216
218→𝜓→→→𝜑𝜓𝜒→𝜑𝜓Modus ponens 208, 217
219→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-2
220→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒Modus ponens 212, 219
221→→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒Subs [𝜑↗→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒] into ax-1
222→𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒Modus ponens 220, 221
223→→𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→→𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→→𝜑𝜓𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗→→→𝜑𝜓𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒𝜒] into ax-2
224→→𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→→𝜑𝜓𝜒𝜒Modus ponens 222, 223
225→𝜓→→→𝜑𝜓𝜒𝜒Modus ponens 218, 224
226→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒Subs [𝜑↗→→𝜑𝜓𝜒] into ax-1
227→→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒Subs [𝜑↗→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1
228→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒Modus ponens 226, 227
229→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓𝜒] into ax-2
230→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒Modus ponens 228, 229
231→→𝜓→→→𝜑𝜓𝜒𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓𝜒] into ax-2
232→→𝜓→→𝜑𝜓𝜒→𝜓𝜒Modus ponens 225, 231
233→→→𝜓→→𝜑𝜓𝜒→𝜓𝜒→→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗→→𝜓→→𝜑𝜓𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1
234→→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒Modus ponens 232, 233
235→→→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒→→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→𝜓→→𝜑𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
236→→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓𝜒Modus ponens 234, 235
237→→→𝜑𝜓𝜒→𝜓𝜒Modus ponens 226, 236jarr
238→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒] into id
239→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
240→→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-1
241→𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 239, 240
242→→𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2
243→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 241, 242
244→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 208, 243
245→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
246→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 238, 245
247→→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-1
248→𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 246, 247
249→→𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2
250→→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 248, 249
251→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 244, 250
252→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒] into ax-1
253→→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
254→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒Modus ponens 252, 253
255→→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→→𝜑𝜓→𝜑𝜒] into ax-2
256→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒Modus ponens 254, 255
257→→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜒] into ax-2
258→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Modus ponens 251, 257
259→→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Subs [𝜑↗→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
260→→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Modus ponens 258, 259
261→→→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2
262→→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Modus ponens 260, 261
263→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Modus ponens 252, 262
264→𝜑→→𝜑𝜒𝜒Subs [𝜓↗𝜒] into pm2.27
265→→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒Subs [𝜑↗→𝜑→→𝜑𝜒𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
266→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒Modus ponens 264, 265
267→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Subs [𝜑↗→𝜓→𝜑𝜒, 𝜓↗𝜑] into ax-1
268→→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Subs [𝜑↗→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
269→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Modus ponens 267, 268
270→→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓→𝜑𝜒] into ax-2
271→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Modus ponens 269, 270
272→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Modus ponens 263, 271
273→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒, 𝜒↗𝜓] into imim2
274→→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒→𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
275→𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒Modus ponens 273, 274
276→→𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2
277→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Modus ponens 275, 276
278→→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
279→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Modus ponens 277, 278
280→→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2
281→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Modus ponens 279, 280
282→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Modus ponens 266, 281
283→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜓𝜒] into ax-2
284→→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
285→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 283, 284
286→→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜒↗→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒] into ax-2
287→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 285, 286
288→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 282, 287
289→→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
290→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 288, 289
291→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 272, 290pm2.86
292→→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑Subs [𝜒↗→𝜓𝜑] into jarr
293→→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜓Subs [𝜑↗→𝜓𝜓, 𝜓↗→→𝜑𝜓→𝜓𝜑] into ax-1
294→→→𝜑𝜓→𝜓𝜑→𝜓𝜓Modus ponens 10, 293
295→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑Subs [𝜑↗𝜓, 𝜒↗𝜑] into ax-2
296→→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑Subs [𝜑↗→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑, 𝜓↗→→𝜑𝜓→𝜓𝜑] into ax-1
297→→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑Modus ponens 295, 296
298→→→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑Subs [𝜑↗→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓→𝜓𝜑, 𝜒↗→→𝜓𝜓→𝜓𝜑] into ax-2
299→→→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑Modus ponens 297, 298
300→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑Modus ponens 292, 299
301→→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→→𝜑𝜓→𝜓𝜑→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜑Subs [𝜑↗→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜓, 𝜒↗→𝜓𝜑] into ax-2
302→→→→𝜑𝜓→𝜓𝜑→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜑Modus ponens 300, 301
303→→→𝜑𝜓→𝜓𝜑→𝜓𝜑Modus ponens 294, 302loolin
304→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-2
305→→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
306→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 304, 305
307→→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→→𝜓𝜑→𝜓𝜒] into ax-2
308→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 306, 307
309→→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 263, 308loowoz
310→¬𝜑¬𝜑Subs [𝜑↗¬𝜑] into id
311→¬𝜑→¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into ax-1
312→→¬𝜑→¬𝜓¬𝜑→¬𝜑→¬𝜑→¬𝜓¬𝜑Subs [𝜑↗→¬𝜑→¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
313→¬𝜑→¬𝜑→¬𝜓¬𝜑Modus ponens 311, 312
314→→¬𝜑→¬𝜑→¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2
315→→¬𝜑¬𝜑→¬𝜑→¬𝜓¬𝜑Modus ponens 313, 314
316→→¬𝜓¬𝜑→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-3
317→→→¬𝜓¬𝜑→𝜑𝜓→¬𝜑→→¬𝜓¬𝜑→𝜑𝜓Subs [𝜑↗→→¬𝜓¬𝜑→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
318→¬𝜑→→¬𝜓¬𝜑→𝜑𝜓Modus ponens 316, 317
319→→¬𝜑→→¬𝜓¬𝜑→𝜑𝜓→→¬𝜑→¬𝜓¬𝜑→¬𝜑→𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2
320→→¬𝜑→¬𝜓¬𝜑→¬𝜑→𝜑𝜓Modus ponens 318, 319
321→¬𝜑→𝜑𝜓Modus ponens 311, 320pm2.21
322→𝜑→¬𝜑𝜑Subs [𝜓↗¬𝜑] into ax-1
323→→𝜑→¬𝜑𝜑→𝜑→𝜑→¬𝜑𝜑Subs [𝜑↗→𝜑→¬𝜑𝜑, 𝜓↗𝜑] into ax-1
324→𝜑→𝜑→¬𝜑𝜑Modus ponens 322, 323
325→→𝜑→𝜑→¬𝜑𝜑→→𝜑𝜑→𝜑→¬𝜑𝜑Subs [𝜓↗𝜑, 𝜒↗→¬𝜑𝜑] into ax-2
326→→𝜑𝜑→𝜑→¬𝜑𝜑Modus ponens 324, 325
327→→¬𝜑→𝜑𝜓→→¬𝜑𝜑→¬𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
328→→¬𝜑𝜑→¬𝜑𝜓Modus ponens pm2.21, 327
329→→→¬𝜑𝜑→¬𝜑𝜓→𝜑→→¬𝜑𝜑→¬𝜑𝜓Subs [𝜑↗→→¬𝜑𝜑→¬𝜑𝜓, 𝜓↗𝜑] into ax-1
330→𝜑→→¬𝜑𝜑→¬𝜑𝜓Modus ponens 328, 329
331→→𝜑→→¬𝜑𝜑→¬𝜑𝜓→→𝜑→¬𝜑𝜑→𝜑→¬𝜑𝜓Subs [𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑𝜓] into ax-2
332→→𝜑→¬𝜑𝜑→𝜑→¬𝜑𝜓Modus ponens 330, 331
333→𝜑→¬𝜑𝜓Modus ponens 322, 332pm2.24
334→→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
335→¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓Modus ponens 213, 334
336→→¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→→¬𝜑→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒→𝜑𝜓] into ax-2
337→→¬𝜑→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓Modus ponens 335, 336
338→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓Modus ponens pm2.21, 337
339→→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒Subs [𝜑↗→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒, 𝜓↗¬𝜑] into ax-1
340→¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒Modus ponens 220, 339
341→→¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒𝜒Subs [𝜑↗¬𝜑, 𝜓↗→→→𝜑𝜓𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒𝜒] into ax-2
342→→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒𝜒Modus ponens 340, 341
343→¬𝜑→→→𝜑𝜓𝜒𝜒Modus ponens 338, 342
344→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗¬𝜑] into ax-1
345→→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒Subs [𝜑↗→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1
346→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒Modus ponens 344, 345
347→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→¬𝜑→→𝜑𝜓𝜒] into ax-2
348→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒Modus ponens 346, 347
349→→¬𝜑→→→𝜑𝜓𝜒𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-2
350→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒Modus ponens 343, 349
351→→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒→→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒Subs [𝜑↗→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1
352→→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒Modus ponens 350, 351
353→→→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒→→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑𝜒Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→¬𝜑→→𝜑𝜓𝜒, 𝜒↗→¬𝜑𝜒] into ax-2
354→→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑𝜒Modus ponens 352, 353
355→→→𝜑𝜓𝜒→¬𝜑𝜒Modus ponens 344, 354jarl
356→→¬𝜑𝜑→¬𝜑𝜑Subs [𝜑↗→¬𝜑𝜑] into id
357→¬𝜑→𝜑¬→¬𝜑𝜑Subs [𝜓↗¬→¬𝜑𝜑] into pm2.21
358→→¬𝜑→𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗¬→¬𝜑𝜑] into ax-2
359→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑Modus ponens 357, 358
360→→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑Subs [𝜑↗→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑] into ax-1
361→→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑Modus ponens 359, 360
362→→→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑¬→¬𝜑𝜑] into ax-2
363→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑Modus ponens 361, 362
364→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑Subs [𝜓↗→¬𝜑𝜑] into ax-3
365→→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑→→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑Subs [𝜑↗→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑, 𝜓↗→¬𝜑𝜑] into ax-1
366→→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑Modus ponens 364, 365
367→→→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑→→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑𝜑Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑¬→¬𝜑𝜑, 𝜒↗→→¬𝜑𝜑𝜑] into ax-2
368→→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑𝜑Modus ponens 366, 367
369→→¬𝜑𝜑→→¬𝜑𝜑𝜑Modus ponens 359, 368
370→→→¬𝜑𝜑→→¬𝜑𝜑𝜑→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑𝜑Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗𝜑] into ax-2
371→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑𝜑Modus ponens 369, 370
372→→¬𝜑𝜑𝜑Modus ponens 356, 371pm2.18
373→¬¬𝜑→¬𝜑𝜑Subs [𝜑↗¬𝜑, 𝜓↗𝜑] into pm2.21
374→→→¬𝜑𝜑𝜑→¬¬𝜑→→¬𝜑𝜑𝜑Subs [𝜑↗→→¬𝜑𝜑𝜑, 𝜓↗¬¬𝜑] into ax-1
375→¬¬𝜑→→¬𝜑𝜑𝜑Modus ponens pm2.18, 374
376→→¬¬𝜑→→¬𝜑𝜑𝜑→→¬¬𝜑→¬𝜑𝜑→¬¬𝜑𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗𝜑] into ax-2
377→→¬¬𝜑→¬𝜑𝜑→¬¬𝜑𝜑Modus ponens 375, 376
378→¬¬𝜑𝜑Modus ponens 373, 377notnotr
379→→𝜑¬𝜓→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓] into id
380→𝜑→→𝜑¬𝜓𝜑Subs [𝜓↗→𝜑¬𝜓] into ax-1
381→→𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→𝜑→→𝜑¬𝜓𝜑Subs [𝜑↗→𝜑→→𝜑¬𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1
382→¬¬𝜑→𝜑→→𝜑¬𝜓𝜑Modus ponens 380, 381
383→→¬¬𝜑→𝜑→→𝜑¬𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→→𝜑¬𝜓𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑¬𝜓𝜑] into ax-2
384→→¬¬𝜑𝜑→¬¬𝜑→→𝜑¬𝜓𝜑Modus ponens 382, 383
385→¬¬𝜑→→𝜑¬𝜓𝜑Modus ponens notnotr, 384
386→→→𝜑¬𝜓→𝜑¬𝜓→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗¬𝜓] into ax-2
387→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓Modus ponens 379, 386
388→→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓→¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓Subs [𝜑↗→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓, 𝜓↗¬¬𝜑] into ax-1
389→¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓Modus ponens 387, 388
390→→¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓→→¬¬𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→→𝜑¬𝜓¬𝜓Subs [𝜑↗¬¬𝜑, 𝜓↗→→𝜑¬𝜓𝜑, 𝜒↗→→𝜑¬𝜓¬𝜓] into ax-2
391→→¬¬𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→→𝜑¬𝜓¬𝜓Modus ponens 389, 390
392→¬¬𝜑→→𝜑¬𝜓¬𝜓Modus ponens 385, 391
393→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬𝜑] into ax-1
394→→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓Subs [𝜑↗→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
395→→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓Modus ponens 393, 394
396→→→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→¬¬𝜑→𝜑¬𝜓] into ax-2
397→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓Modus ponens 395, 396
398→→¬¬𝜑→→𝜑¬𝜓¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬𝜓] into ax-2
399→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓Modus ponens 392, 398
400→→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓Subs [𝜑↗→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
401→→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓Modus ponens 399, 400
402→→→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓→→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬¬𝜑→𝜑¬𝜓, 𝜒↗→¬¬𝜑¬𝜓] into ax-2
403→→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑¬𝜓Modus ponens 401, 402
404→→𝜑¬𝜓→¬¬𝜑¬𝜓Modus ponens 393, 403
405→→¬¬𝜑¬𝜓→𝜓¬𝜑Subs [𝜑↗¬𝜑] into ax-3
406→→→¬¬𝜑¬𝜓→𝜓¬𝜑→→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑Subs [𝜑↗→→¬¬𝜑¬𝜓→𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
407→→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑Modus ponens 405, 406
408→→→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑→→→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬¬𝜑¬𝜓, 𝜒↗→𝜓¬𝜑] into ax-2
409→→→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→𝜓¬𝜑Modus ponens 407, 408
410→→𝜑¬𝜓→𝜓¬𝜑Modus ponens 404, 409con2
411→→¬𝜑¬𝜑→𝜑→¬𝜑¬𝜑Subs [𝜑↗→¬𝜑¬𝜑, 𝜓↗𝜑] into ax-1
412→𝜑→¬𝜑¬𝜑Modus ponens 310, 411
413→¬¬¬𝜑¬𝜑Subs [𝜑↗¬𝜑] into notnotr
414→¬𝜑→𝜑¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗𝜑] into ax-1
415→→¬𝜑→𝜑¬𝜑→¬¬¬𝜑→¬𝜑→𝜑¬𝜑Subs [𝜑↗→¬𝜑→𝜑¬𝜑, 𝜓↗¬¬¬𝜑] into ax-1
416→¬¬¬𝜑→¬𝜑→𝜑¬𝜑Modus ponens 414, 415
417→→¬¬¬𝜑→¬𝜑→𝜑¬𝜑→→¬¬¬𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑Subs [𝜑↗¬¬¬𝜑, 𝜓↗¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2
418→→¬¬¬𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑Modus ponens 416, 417
419→¬¬¬𝜑→𝜑¬𝜑Modus ponens 413, 418
420→→𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→𝜑¬𝜑Subs [𝜓↗¬𝜑, 𝜒↗¬𝜑] into ax-2
421→→𝜑¬𝜑→𝜑¬𝜑Modus ponens 412, 420
422→→→𝜑¬𝜑→𝜑¬𝜑→¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜑, 𝜓↗¬¬¬𝜑] into ax-1
423→¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑Modus ponens 421, 422
424→→¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑→→¬¬¬𝜑→𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑Subs [𝜑↗¬¬¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2
425→→¬¬¬𝜑→𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑Modus ponens 423, 424
426→𝜑→¬¬¬𝜑𝜑Subs [𝜓↗¬¬¬𝜑] into ax-1
427→→𝜑→¬¬¬𝜑𝜑→𝜑→𝜑→¬¬¬𝜑𝜑Subs [𝜑↗→𝜑→¬¬¬𝜑𝜑, 𝜓↗𝜑] into ax-1
428→𝜑→𝜑→¬¬¬𝜑𝜑Modus ponens 426, 427
429→→𝜑→𝜑→¬¬¬𝜑𝜑→→𝜑𝜑→𝜑→¬¬¬𝜑𝜑Subs [𝜓↗𝜑, 𝜒↗→¬¬¬𝜑𝜑] into ax-2
430→→𝜑𝜑→𝜑→¬¬¬𝜑𝜑Modus ponens 428, 429
431→→¬¬¬𝜑→𝜑¬𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑Subs [𝜑↗¬¬¬𝜑, 𝜓↗𝜑, 𝜒↗¬𝜑] into ax-2
432→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑Modus ponens 419, 431
433→→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑→𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑Subs [𝜑↗→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑, 𝜓↗𝜑] into ax-1
434→𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑Modus ponens 432, 433
435→→𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑→→𝜑→¬¬¬𝜑𝜑→𝜑→¬¬¬𝜑¬𝜑Subs [𝜓↗→¬¬¬𝜑𝜑, 𝜒↗→¬¬¬𝜑¬𝜑] into ax-2
436→→𝜑→¬¬¬𝜑𝜑→𝜑→¬¬¬𝜑¬𝜑Modus ponens 434, 435
437→𝜑→¬¬¬𝜑¬𝜑Modus ponens 426, 436
438→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑] into ax-3
439→→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑→𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑Subs [𝜑↗→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑, 𝜓↗𝜑] into ax-1
440→𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑Modus ponens 438, 439
441→→𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑→→𝜑→¬¬¬𝜑¬𝜑→𝜑→𝜑¬¬𝜑Subs [𝜓↗→¬¬¬𝜑¬𝜑, 𝜒↗→𝜑¬¬𝜑] into ax-2
442→→𝜑→¬¬¬𝜑¬𝜑→𝜑→𝜑¬¬𝜑Modus ponens 440, 441
443→𝜑→𝜑¬¬𝜑Modus ponens 437, 442
444→→𝜑→𝜑¬¬𝜑→→𝜑𝜑→𝜑¬¬𝜑Subs [𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
445→→𝜑𝜑→𝜑¬¬𝜑Modus ponens 443, 444
446→𝜑¬¬𝜑Modus ponens id, 445notnot
447→→¬𝜑𝜓→¬𝜑𝜓Subs [𝜑↗→¬𝜑𝜓] into id
448→𝜓¬¬𝜓Subs [𝜑↗𝜓] into notnot
449→→𝜓¬¬𝜓→¬𝜑→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1
450→¬𝜑→𝜓¬¬𝜓Modus ponens 448, 449
451→→¬𝜑→𝜓¬¬𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓Subs [𝜑↗¬𝜑, 𝜒↗¬¬𝜓] into ax-2
452→→¬𝜑𝜓→¬𝜑¬¬𝜓Modus ponens 450, 451
453→→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓Subs [𝜑↗→→¬𝜑𝜓→¬𝜑¬¬𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
454→→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓Modus ponens 452, 453
455→→→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗→¬𝜑¬¬𝜓] into ax-2
456→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓Modus ponens 454, 455
457→→¬𝜑¬¬𝜓→¬𝜓𝜑Subs [𝜓↗¬𝜓] into ax-3
458→→→¬𝜑¬¬𝜓→¬𝜓𝜑→→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑Subs [𝜑↗→→¬𝜑¬¬𝜓→¬𝜓𝜑, 𝜓↗→¬𝜑𝜓] into ax-1
459→→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑Modus ponens 457, 458
460→→→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑→→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→¬𝜓𝜑Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑¬¬𝜓, 𝜒↗→¬𝜓𝜑] into ax-2
461→→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→¬𝜓𝜑Modus ponens 459, 460
462→→¬𝜑𝜓→¬𝜓𝜑Modus ponens 452, 461con1
463→→𝜑→→𝜑𝜓𝜑→¬¬𝜑→𝜑→→𝜑𝜓𝜑Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1
464→¬¬𝜑→𝜑→→𝜑𝜓𝜑Modus ponens 25, 463
465→→¬¬𝜑→𝜑→→𝜑𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→→𝜑𝜓𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2
466→→¬¬𝜑𝜑→¬¬𝜑→→𝜑𝜓𝜑Modus ponens 464, 465
467→¬¬𝜑→→𝜑𝜓𝜑Modus ponens notnotr, 466
468→→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗¬¬𝜑] into ax-1
469→¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓Modus ponens 31, 468
470→→¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→¬¬𝜑→→𝜑𝜓𝜑→¬¬𝜑→→𝜑𝜓𝜓Subs [𝜑↗¬¬𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2
471→→¬¬𝜑→→𝜑𝜓𝜑→¬¬𝜑→→𝜑𝜓𝜓Modus ponens 469, 470
472→¬¬𝜑→→𝜑𝜓𝜓Modus ponens 467, 471
473→→𝜑𝜓→¬¬𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬𝜑] into ax-1
474→→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→¬¬𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
475→→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓Modus ponens 473, 474
476→→→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬𝜑→𝜑𝜓] into ax-2
477→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓Modus ponens 475, 476
478→→¬¬𝜑→→𝜑𝜓𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2
479→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓Modus ponens 472, 478
480→→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓Subs [𝜑↗→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
481→→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓Modus ponens 479, 480
482→→→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓→→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→¬¬𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑→𝜑𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2
483→→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→¬¬𝜑𝜓Modus ponens 481, 482
484→→𝜑𝜓→¬¬𝜑𝜓Modus ponens 473, 483
485→→𝜓¬¬𝜓→¬¬𝜑→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜑] into ax-1
486→¬¬𝜑→𝜓¬¬𝜓Modus ponens 448, 485
487→→¬¬𝜑→𝜓¬¬𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗¬¬𝜑, 𝜒↗¬¬𝜓] into ax-2
488→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓Modus ponens 486, 487
489→→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓, 𝜓↗→𝜑𝜓] into ax-1
490→→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓Modus ponens 488, 489
491→→→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2
492→→→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→¬¬𝜑¬¬𝜓Modus ponens 490, 491
493→→𝜑𝜓→¬¬𝜑¬¬𝜓Modus ponens 484, 492
494→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into ax-3
495→→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗→𝜑𝜓] into ax-1
496→→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Modus ponens 494, 495
497→→→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→→𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→¬𝜓¬𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
498→→→𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→¬𝜓¬𝜑Modus ponens 496, 497
499→→𝜑𝜓→¬𝜓¬𝜑Modus ponens 493, 498con3
500→𝜑→→𝜑¬𝜓¬𝜓Subs [𝜓↗¬𝜓] into pm2.27
501→¬¬→𝜑¬𝜓→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓] into notnotr
502→→𝜑¬𝜓→𝜑→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗𝜑] into ax-1
503→→→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓Subs [𝜑↗→→𝜑¬𝜓→𝜑→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into ax-1
504→¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓Modus ponens 502, 503
505→→¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓→→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑→𝜑¬𝜓] into ax-2
506→→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓Modus ponens 504, 505
507→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓Modus ponens 501, 506
508→→𝜑→→𝜑¬𝜓¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓Subs [𝜓↗→𝜑¬𝜓, 𝜒↗¬𝜓] into ax-2
509→→𝜑→𝜑¬𝜓→𝜑¬𝜓Modus ponens 500, 508
510→→→𝜑→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓Subs [𝜑↗→→𝜑→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into ax-1
511→¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓Modus ponens 509, 510
512→→¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓→→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
513→→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓Modus ponens 511, 512
514→𝜑→¬¬→𝜑¬𝜓𝜑Subs [𝜓↗¬¬→𝜑¬𝜓] into ax-1
515→→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→𝜑→¬¬→𝜑¬𝜓𝜑Subs [𝜑↗→𝜑→¬¬→𝜑¬𝜓𝜑, 𝜓↗𝜑] into ax-1
516→𝜑→𝜑→¬¬→𝜑¬𝜓𝜑Modus ponens 514, 515
517→→𝜑→𝜑→¬¬→𝜑¬𝜓𝜑→→𝜑𝜑→𝜑→¬¬→𝜑¬𝜓𝜑Subs [𝜓↗𝜑, 𝜒↗→¬¬→𝜑¬𝜓𝜑] into ax-2
518→→𝜑𝜑→𝜑→¬¬→𝜑¬𝜓𝜑Modus ponens 516, 517
519→→¬¬→𝜑¬𝜓→𝜑¬𝜓→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗¬𝜓] into ax-2
520→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓Modus ponens 501, 519
521→→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓Subs [𝜑↗→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1
522→𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓Modus ponens 520, 521
523→→𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓→→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→¬¬→𝜑¬𝜓¬𝜓Subs [𝜓↗→¬¬→𝜑¬𝜓𝜑, 𝜒↗→¬¬→𝜑¬𝜓¬𝜓] into ax-2
524→→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→¬¬→𝜑¬𝜓¬𝜓Modus ponens 522, 523
525→𝜑→¬¬→𝜑¬𝜓¬𝜓Modus ponens 514, 524
526→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓] into ax-3
527→→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓→𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓, 𝜓↗𝜑] into ax-1
528→𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓Modus ponens 526, 527
529→→𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓→→𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→𝜓¬→𝜑¬𝜓Subs [𝜓↗→¬¬→𝜑¬𝜓¬𝜓, 𝜒↗→𝜓¬→𝜑¬𝜓] into ax-2
530→→𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→𝜓¬→𝜑¬𝜓Modus ponens 528, 529
531→𝜑→𝜓¬→𝜑¬𝜓Modus ponens 525, 530pm3.2im
532→¬¬→𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓] into notnotr
533→→𝜑𝜓→𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑] into ax-1
534→→→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
535→¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓Modus ponens 533, 534
536→→¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜑→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into ax-2
537→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜑→𝜑𝜓Modus ponens 535, 536
538→¬¬→𝜑𝜓→𝜑→𝜑𝜓Modus ponens 532, 537
539→→→𝜑→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓Subs [𝜑↗→→𝜑→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
540→¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓Modus ponens pm2.43, 539
541→→¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓→→¬¬→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
542→→¬¬→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→𝜑𝜓Modus ponens 540, 541
543→𝜑→¬¬→𝜑𝜓𝜑Subs [𝜓↗¬¬→𝜑𝜓] into ax-1
544→→𝜑→¬¬→𝜑𝜓𝜑→𝜑→𝜑→¬¬→𝜑𝜓𝜑Subs [𝜑↗→𝜑→¬¬→𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1
545→𝜑→𝜑→¬¬→𝜑𝜓𝜑Modus ponens 543, 544
546→→𝜑→𝜑→¬¬→𝜑𝜓𝜑→→𝜑𝜑→𝜑→¬¬→𝜑𝜓𝜑Subs [𝜓↗𝜑, 𝜒↗→¬¬→𝜑𝜓𝜑] into ax-2
547→→𝜑𝜑→𝜑→¬¬→𝜑𝜓𝜑Modus ponens 545, 546
548→→¬¬→𝜑𝜓→𝜑𝜓→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
549→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓Modus ponens 532, 548
550→→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓→𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓Subs [𝜑↗→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
551→𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓Modus ponens 549, 550
552→→𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓→→𝜑→¬¬→𝜑𝜓𝜑→𝜑→¬¬→𝜑𝜓𝜓Subs [𝜓↗→¬¬→𝜑𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓𝜓] into ax-2
553→→𝜑→¬¬→𝜑𝜓𝜑→𝜑→¬¬→𝜑𝜓𝜓Modus ponens 551, 552
554→𝜑→¬¬→𝜑𝜓𝜓Modus ponens 543, 553
555→→𝜓¬¬𝜓→¬¬→𝜑𝜓→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
556→¬¬→𝜑𝜓→𝜓¬¬𝜓Modus ponens 448, 555
557→→¬¬→𝜑𝜓→𝜓¬¬𝜓→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜒↗¬¬𝜓] into ax-2
558→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓Modus ponens 556, 557
559→→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓→𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓Subs [𝜑↗→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1
560→𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓Modus ponens 558, 559
561→→𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓→→𝜑→¬¬→𝜑𝜓𝜓→𝜑→¬¬→𝜑𝜓¬¬𝜓Subs [𝜓↗→¬¬→𝜑𝜓𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬𝜓] into ax-2
562→→𝜑→¬¬→𝜑𝜓𝜓→𝜑→¬¬→𝜑𝜓¬¬𝜓Modus ponens 560, 561
563→𝜑→¬¬→𝜑𝜓¬¬𝜓Modus ponens 554, 562
564→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-3
565→→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓→𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓Subs [𝜑↗→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓, 𝜓↗𝜑] into ax-1
566→𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓Modus ponens 564, 565
567→→𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓→→𝜑→¬¬→𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬→𝜑𝜓Subs [𝜓↗→¬¬→𝜑𝜓¬¬𝜓, 𝜒↗→¬𝜓¬→𝜑𝜓] into ax-2
568→→𝜑→¬¬→𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬→𝜑𝜓Modus ponens 566, 567
569→𝜑→¬𝜓¬→𝜑𝜓Modus ponens 563, 568jcn
570→¬¬𝜓𝜓Subs [𝜑↗𝜓] into notnotr
571→→𝜓→𝜑𝜓→¬¬𝜓→𝜓→𝜑𝜓Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
572→¬¬𝜓→𝜓→𝜑𝜓Modus ponens 208, 571
573→→¬¬𝜓→𝜓→𝜑𝜓→→¬¬𝜓𝜓→¬¬𝜓→𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜒↗→𝜑𝜓] into ax-2
574→→¬¬𝜓𝜓→¬¬𝜓→𝜑𝜓Modus ponens 572, 573
575→¬¬𝜓→𝜑𝜓Modus ponens 570, 574
576→→𝜑→𝜓𝜓→→𝜑𝜓→𝜑𝜓Subs [𝜒↗𝜓] into ax-2
577→→→𝜑𝜓→𝜑𝜓→¬¬𝜓→→𝜑𝜓→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
578→¬¬𝜓→→𝜑𝜓→𝜑𝜓Modus ponens 24, 577
579→→¬¬𝜓→→𝜑𝜓→𝜑𝜓→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
580→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜓Modus ponens 578, 579
581→𝜑→¬¬𝜓𝜑Subs [𝜓↗¬¬𝜓] into ax-1
582→→𝜑→¬¬𝜓𝜑→𝜑→𝜑→¬¬𝜓𝜑Subs [𝜑↗→𝜑→¬¬𝜓𝜑, 𝜓↗𝜑] into ax-1
583→𝜑→𝜑→¬¬𝜓𝜑Modus ponens 581, 582
584→→𝜑→𝜑→¬¬𝜓𝜑→→𝜑𝜑→𝜑→¬¬𝜓𝜑Subs [𝜓↗𝜑, 𝜒↗→¬¬𝜓𝜑] into ax-2
585→→𝜑𝜑→𝜑→¬¬𝜓𝜑Modus ponens 583, 584
586→→¬¬𝜓→𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
587→→¬¬𝜓𝜑→¬¬𝜓𝜓Modus ponens 575, 586
588→→→¬¬𝜓𝜑→¬¬𝜓𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓𝜓, 𝜓↗𝜑] into ax-1
589→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓Modus ponens 587, 588
590→→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜓Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓𝜓] into ax-2
591→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜓Modus ponens 589, 590
592→𝜑→¬¬𝜓𝜓Modus ponens 581, 591
593→→𝜓¬¬𝜓→¬¬𝜓→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1
594→¬¬𝜓→𝜓¬¬𝜓Modus ponens 448, 593
595→→¬¬𝜓→𝜓¬¬𝜓→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓Subs [𝜑↗¬¬𝜓, 𝜒↗¬¬𝜓] into ax-2
596→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓Modus ponens 594, 595
597→→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓→𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓Subs [𝜑↗→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1
598→𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓Modus ponens 596, 597
599→→𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓→→𝜑→¬¬𝜓𝜓→𝜑→¬¬𝜓¬¬𝜓Subs [𝜓↗→¬¬𝜓𝜓, 𝜒↗→¬¬𝜓¬¬𝜓] into ax-2
600→→𝜑→¬¬𝜓𝜓→𝜑→¬¬𝜓¬¬𝜓Modus ponens 598, 599
601→𝜑→¬¬𝜓¬¬𝜓Modus ponens 592, 600
602→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓] into ax-3
603→→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓→𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1
604→𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓Modus ponens 602, 603
605→→𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓→→𝜑→¬¬𝜓¬¬𝜓→𝜑→¬𝜓¬𝜓Subs [𝜓↗→¬¬𝜓¬¬𝜓, 𝜒↗→¬𝜓¬𝜓] into ax-2
606→→𝜑→¬¬𝜓¬¬𝜓→𝜑→¬𝜓¬𝜓Modus ponens 604, 605
607→𝜑→¬𝜓¬𝜓Modus ponens 601, 606
608→¬𝜓¬𝜓Subs [𝜑↗¬𝜓] into id
609→¬𝜓→𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗𝜑] into ax-1
610→→¬𝜓→𝜑¬𝜓→¬𝜓→¬𝜓→𝜑¬𝜓Subs [𝜑↗→¬𝜓→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
611→¬𝜓→¬𝜓→𝜑¬𝜓Modus ponens 609, 610
612→→¬𝜓→¬𝜓→𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
613→→¬𝜓¬𝜓→¬𝜓→𝜑¬𝜓Modus ponens 611, 612
614→→𝜑→¬𝜓¬𝜓→→𝜑¬𝜓→𝜑¬𝜓Subs [𝜓↗¬𝜓, 𝜒↗¬𝜓] into ax-2
615→→→𝜑¬𝜓→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓→𝜑¬𝜓Subs [𝜑↗→→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
616→¬𝜓→→𝜑¬𝜓→𝜑¬𝜓Modus ponens 379, 615
617→→¬𝜓→→𝜑¬𝜓→𝜑¬𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
618→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬𝜓Modus ponens 616, 617
619→¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓] into id
620→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
621→¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 619, 620
622→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓] into notnotr
623→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
624→→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
625→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Modus ponens 623, 624
626→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬𝜓¬→𝜑¬𝜓] into ax-2
627→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Modus ponens 625, 626
628→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Modus ponens 622, 627
629→→¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
630→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Modus ponens 621, 629
631→→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
632→¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Modus ponens 630, 631
633→→¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬𝜓¬→𝜑¬𝜓, 𝜒↗→¬𝜓¬→𝜑¬𝜓] into ax-2
634→→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓Modus ponens 632, 633
635→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
636→→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
637→¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓Modus ponens 635, 636
638→→¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬𝜓] into ax-2
639→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓Modus ponens 637, 638
640→→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
641→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 628, 640
642→→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
643→¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 641, 642
644→→¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
645→→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 643, 644
646→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 635, 645
647→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-3
648→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
649→¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 647, 648
650→→¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
651→→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 649, 650
652→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 646, 651
653→→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
654→→¬𝜓→𝜑¬𝜓→¬𝜓¬¬→𝜑¬𝜓Modus ponens 652, 653
655→¬𝜓¬¬→𝜑¬𝜓Modus ponens 609, 654
656→→¬𝜓¬¬→𝜑¬𝜓→¬→𝜑¬𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-3
657→¬→𝜑¬𝜓𝜓Modus ponens 655, 656simprim
658→¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓] into id
659→→¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
660→¬𝜑→¬→𝜑𝜓¬→𝜑𝜓Modus ponens 658, 659
661→¬¬¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓] into notnotr
662→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
663→→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
664→¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Modus ponens 662, 663
665→→¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬𝜑¬→𝜑𝜓] into ax-2
666→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Modus ponens 664, 665
667→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Modus ponens 661, 666
668→→¬𝜑→¬→𝜑𝜓¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
669→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Modus ponens 660, 668
670→→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Subs [𝜑↗→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
671→¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Modus ponens 669, 670
672→→¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗→¬𝜑¬→𝜑𝜓, 𝜒↗→¬𝜑¬→𝜑𝜓] into ax-2
673→→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓Modus ponens 671, 672
674→¬𝜑→¬¬¬→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
675→→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
676→¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑Modus ponens 674, 675
677→→¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑𝜓¬𝜑] into ax-2
678→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑Modus ponens 676, 677
679→→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬→𝜑𝜓] into ax-2
680→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓Modus ponens 667, 679
681→→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
682→¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓Modus ponens 680, 681
683→→¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑𝜓¬𝜑, 𝜒↗→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-2
684→→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓Modus ponens 682, 683
685→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓Modus ponens 674, 684
686→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-3
687→→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
688→¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓Modus ponens 686, 687
689→→¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬¬→𝜑𝜓] into ax-2
690→→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓Modus ponens 688, 689
691→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓Modus ponens 685, 690
692→→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓→→¬𝜑→𝜑𝜓→¬𝜑¬¬→𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
693→→¬𝜑→𝜑𝜓→¬𝜑¬¬→𝜑𝜓Modus ponens 691, 692
694→¬𝜑¬¬→𝜑𝜓Modus ponens pm2.21, 693
695→→¬𝜑¬¬→𝜑𝜓→¬→𝜑𝜓𝜑Subs [𝜓↗¬→𝜑𝜓] into ax-3
696→¬→𝜑𝜓𝜑Modus ponens 694, 695simplim
697→𝜑→¬𝜒𝜑Subs [𝜓↗¬𝜒] into ax-1
698→→𝜑→¬𝜒𝜑→¬→𝜑𝜓→𝜑→¬𝜒𝜑Subs [𝜑↗→𝜑→¬𝜒𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
699→¬→𝜑𝜓→𝜑→¬𝜒𝜑Modus ponens 697, 698
700→→¬→𝜑𝜓→𝜑→¬𝜒𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→¬𝜒𝜑Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗→¬𝜒𝜑] into ax-2
701→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→¬𝜒𝜑Modus ponens 699, 700
702→¬→𝜑𝜓→¬𝜒𝜑Modus ponens simplim, 701
703→→𝜑¬¬𝜑→¬𝜒→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬𝜒] into ax-1
704→¬𝜒→𝜑¬¬𝜑Modus ponens notnot, 703
705→→¬𝜒→𝜑¬¬𝜑→→¬𝜒𝜑→¬𝜒¬¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
706→→¬𝜒𝜑→¬𝜒¬¬𝜑Modus ponens 704, 705
707→→→¬𝜒𝜑→¬𝜒¬¬𝜑→¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑Subs [𝜑↗→→¬𝜒𝜑→¬𝜒¬¬𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
708→¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑Modus ponens 706, 707
709→→¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑→→¬→𝜑𝜓→¬𝜒𝜑→¬→𝜑𝜓→¬𝜒¬¬𝜑Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒𝜑, 𝜒↗→¬𝜒¬¬𝜑] into ax-2
710→→¬→𝜑𝜓→¬𝜒𝜑→¬→𝜑𝜓→¬𝜒¬¬𝜑Modus ponens 708, 709
711→¬→𝜑𝜓→¬𝜒¬¬𝜑Modus ponens 702, 710
712→→¬𝜒¬¬𝜑→¬𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗¬𝜑] into ax-3
713→→→¬𝜒¬¬𝜑→¬𝜑𝜒→¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒Subs [𝜑↗→→¬𝜒¬¬𝜑→¬𝜑𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
714→¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒Modus ponens 712, 713
715→→¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒→→¬→𝜑𝜓→¬𝜒¬¬𝜑→¬→𝜑𝜓→¬𝜑𝜒Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒¬¬𝜑, 𝜒↗→¬𝜑𝜒] into ax-2
716→→¬→𝜑𝜓→¬𝜒¬¬𝜑→¬→𝜑𝜓→¬𝜑𝜒Modus ponens 714, 715
717→¬→𝜑𝜓→¬𝜑𝜒Modus ponens 711, 716pm2.5g
718→¬→𝜑𝜓→¬𝜑𝜓Subs [𝜒↗𝜓] into pm2.5gpm2.5
719→→¬→𝜑𝜓¬→𝜑𝜓→𝜓→¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓¬→𝜑𝜓] into ax-1
720→𝜓→¬→𝜑𝜓¬→𝜑𝜓Modus ponens 658, 719
721→¬→𝜑𝜓→𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓] into ax-1
722→→¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓→𝜓¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
723→¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓Modus ponens 721, 722
724→→¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→𝜓¬→𝜑𝜓] into ax-2
725→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓Modus ponens 723, 724
726→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓Modus ponens 661, 725
727→→𝜓→¬→𝜑𝜓¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
728→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓Modus ponens 720, 727
729→→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓Subs [𝜑↗→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
730→¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓Modus ponens 728, 729
731→→¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗→𝜓¬→𝜑𝜓, 𝜒↗→𝜓¬→𝜑𝜓] into ax-2
732→→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓Modus ponens 730, 731
733→𝜓→¬¬¬→𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
734→→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→𝜓→¬¬¬→𝜑𝜓𝜓Subs [𝜑↗→𝜓→¬¬¬→𝜑𝜓𝜓] into ax-1
735→𝜓→𝜓→¬¬¬→𝜑𝜓𝜓Modus ponens 733, 734
736→→𝜓→𝜓→¬¬¬→𝜑𝜓𝜓→→𝜓𝜓→𝜓→¬¬¬→𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜒↗→¬¬¬→𝜑𝜓𝜓] into ax-2
737→→𝜓𝜓→𝜓→¬¬¬→𝜑𝜓𝜓Modus ponens 735, 736
738→→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
739→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓Modus ponens 726, 738
740→→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-1
741→𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓Modus ponens 739, 740
742→→𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→¬¬¬→𝜑𝜓𝜓, 𝜒↗→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-2
743→→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓Modus ponens 741, 742
744→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓Modus ponens 733, 743
745→→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓] into ax-1
746→𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓Modus ponens 686, 745
747→→𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬¬→𝜑𝜓] into ax-2
748→→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→𝜑𝜓¬¬→𝜑𝜓Modus ponens 746, 747
749→𝜓→→𝜑𝜓¬¬→𝜑𝜓Modus ponens 744, 748
750→→𝜓→→𝜑𝜓¬¬→𝜑𝜓→→𝜓→𝜑𝜓→𝜓¬¬→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
751→→𝜓→𝜑𝜓→𝜓¬¬→𝜑𝜓Modus ponens 749, 750
752→𝜓¬¬→𝜑𝜓Modus ponens 208, 751
753→→𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬¬→𝜑𝜓Subs [𝜑↗→𝜓¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
754→¬→𝜑𝜓→𝜓¬¬→𝜑𝜓Modus ponens 752, 753
755→𝜓→¬→𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
756→→𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→𝜓→¬→𝜑𝜓𝜓Subs [𝜑↗→𝜓→¬→𝜑𝜓𝜓, 𝜓↗¬¬𝜓] into ax-1
757→¬¬𝜓→𝜓→¬→𝜑𝜓𝜓Modus ponens 755, 756
758→→¬¬𝜓→𝜓→¬→𝜑𝜓𝜓→→¬¬𝜓𝜓→¬¬𝜓→¬→𝜑𝜓𝜓Subs [𝜑↗¬¬𝜓, 𝜒↗→¬→𝜑𝜓𝜓] into ax-2
759→→¬¬𝜓𝜓→¬¬𝜓→¬→𝜑𝜓𝜓Modus ponens 757, 758
760→¬¬𝜓→¬→𝜑𝜓𝜓Modus ponens 570, 759
761→→¬→𝜑𝜓→𝜓¬¬→𝜑𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
762→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓Modus ponens 754, 761
763→→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
764→¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓Modus ponens 762, 763
765→→¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗→¬→𝜑𝜓𝜓, 𝜒↗→¬→𝜑𝜓¬¬→𝜑𝜓] into ax-2
766→→¬¬𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓Modus ponens 764, 765
767→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓Modus ponens 760, 766
768→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
769→→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
770→¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓Modus ponens 768, 769
771→→¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬𝜓¬→𝜑𝜓] into ax-2
772→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓Modus ponens 770, 771
773→→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
774→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓Modus ponens 767, 773
775→→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓Subs [𝜑↗→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
776→¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓Modus ponens 774, 775
777→→¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬𝜓¬→𝜑𝜓, 𝜒↗→¬¬𝜓¬¬→𝜑𝜓] into ax-2
778→→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓Modus ponens 776, 777
779→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓Modus ponens 768, 778
780→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-3
781→→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
782→¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓Modus ponens 780, 781
783→→¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬𝜓¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬𝜓] into ax-2
784→→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓Modus ponens 782, 783
785→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓Modus ponens 779, 784
786→→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓¬𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬𝜓] into ax-2
787→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓¬𝜓Modus ponens 785, 786
788→¬→𝜑𝜓¬𝜓Modus ponens 658, 787conax1
789→¬𝜓→𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗𝜒] into ax-1
790→→¬𝜓→𝜒¬𝜓→¬→𝜑𝜓→¬𝜓→𝜒¬𝜓Subs [𝜑↗→¬𝜓→𝜒¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
791→¬→𝜑𝜓→¬𝜓→𝜒¬𝜓Modus ponens 789, 790
792→→¬→𝜑𝜓→¬𝜓→𝜒¬𝜓→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→𝜒¬𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜒¬𝜓] into ax-2
793→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→𝜒¬𝜓Modus ponens 791, 792
794→¬→𝜑𝜓→𝜒¬𝜓Modus ponens conax1, 793conax1k
795→¬→𝜑𝜓→𝜑¬𝜓Subs [𝜒↗𝜑] into conax1kpm2.51
796→¬→𝜑𝜓→¬𝜑¬𝜓Subs [𝜒↗¬𝜑] into conax1kpm2.52
797→¬𝜓→¬𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜒] into ax-1
798→→¬𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓Subs [𝜑↗→¬𝜓→¬𝜒¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
799→¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓Modus ponens 797, 798
800→→¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→¬𝜒¬𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗→¬𝜒¬𝜓] into ax-2
801→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→¬𝜒¬𝜓Modus ponens 799, 800
802→¬→𝜑𝜓→¬𝜒¬𝜓Modus ponens conax1, 801
803→→¬𝜒¬𝜓→𝜓𝜒Subs [𝜑↗𝜒] into ax-3
804→→→¬𝜒¬𝜓→𝜓𝜒→¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒Subs [𝜑↗→→¬𝜒¬𝜓→𝜓𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
805→¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒Modus ponens 803, 804
806→→¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒→→¬→𝜑𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→𝜓𝜒Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒¬𝜓, 𝜒↗→𝜓𝜒] into ax-2
807→→¬→𝜑𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→𝜓𝜒Modus ponens 805, 806
808→¬→𝜑𝜓→𝜓𝜒Modus ponens 802, 807pm2.521g
809→→𝜑→𝜒𝜑→¬→𝜑𝜓→𝜑→𝜒𝜑Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
810→¬→𝜑𝜓→𝜑→𝜒𝜑Modus ponens 13, 809
811→→¬→𝜑𝜓→𝜑→𝜒𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→𝜒𝜑Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2
812→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→𝜒𝜑Modus ponens 810, 811
813→¬→𝜑𝜓→𝜒𝜑Modus ponens simplim, 812pm2.521g2
814→¬→𝜑𝜓→𝜓𝜑Subs [𝜒↗𝜑] into pm2.521gpm2.521
815→𝜑→𝜒𝜒Subs [𝜓↗𝜒] into idd
816→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒Subs [𝜑↗→𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
817→→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒Subs [𝜑↗→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1
818→𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒Modus ponens 816, 817
819→→𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→¬→𝜑¬𝜓→𝜒𝜒Subs [𝜓↗→𝜒𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜒𝜒] into ax-2
820→→𝜑→𝜒𝜒→𝜑→¬→𝜑¬𝜓→𝜒𝜒Modus ponens 818, 819
821→𝜑→¬→𝜑¬𝜓→𝜒𝜒Modus ponens 815, 820
822→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜒] into ax-2
823→→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒Subs [𝜑↗→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒, 𝜓↗𝜑] into ax-1
824→𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒Modus ponens 822, 823
825→→𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒Subs [𝜓↗→¬→𝜑¬𝜓→𝜒𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒] into ax-2
826→→𝜑→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒Modus ponens 824, 825
827→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒Modus ponens 821, 826
828→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓Subs [𝜑↗→𝜓¬→𝜑¬𝜓, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1
829→→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓, 𝜓↗𝜑] into ax-1
830→𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓Modus ponens 828, 829
831→→𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓] into ax-2
832→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓Modus ponens 830, 831
833→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓Modus ponens pm3.2im, 832
834→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into imim2
835→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Subs [𝜑↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1
836→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Modus ponens 834, 835
837→→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→→𝜓¬→𝜑¬𝜓→𝜓𝜒] into ax-2
838→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Modus ponens 836, 837
839→→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Subs [𝜑↗→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗𝜑] into ax-1
840→𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Modus ponens 838, 839
841→→𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒] into ax-2
842→→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Modus ponens 840, 841
843→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒Modus ponens 827, 842
844→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓𝜒] into ax-2
845→→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒Subs [𝜑↗→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
846→𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒Modus ponens 844, 845
847→→𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜒↗→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒] into ax-2
848→→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒Modus ponens 846, 847
849→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒Modus ponens 843, 848
850→→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓, 𝜒↗→→¬→𝜑¬𝜓𝜒→𝜓𝜒] into ax-2
851→→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒Modus ponens 849, 850
852→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒Modus ponens 833, 851
853→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜓𝜒] into id
854→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗𝜑] into ax-1
855→→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒Subs [𝜑↗→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1
856→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒Modus ponens 854, 855
857→→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜑→¬→𝜑¬𝜓𝜒] into ax-2
858→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒Modus ponens 856, 857
859→→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒Subs [𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
860→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒Modus ponens 852, 859
861→→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1
862→→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒Modus ponens 860, 861
863→→→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜑→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
864→→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒Modus ponens 862, 863
865→→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒Modus ponens 854, 864expt
866→¬→𝜑¬𝜓𝜑Subs [𝜓↗¬𝜓] into simplim
867→→𝜓𝜒→𝜓𝜒Subs [𝜑↗→𝜓𝜒] into id
868→→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→𝜓𝜒Subs [𝜑↗→→𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
869→𝜑→→𝜓𝜒→𝜓𝜒Modus ponens 867, 868
870→→𝜑→→𝜓𝜒→𝜓𝜒→→𝜑→𝜓𝜒→𝜑→𝜓𝜒Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
871→𝜑→→𝜑→𝜓𝜒𝜑Subs [𝜓↗→𝜑→𝜓𝜒] into ax-1
872→→𝜑→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑Subs [𝜑↗→𝜑→→𝜑→𝜓𝜒𝜑, 𝜓↗¬→𝜑¬𝜓] into ax-1
873→¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑Modus ponens 871, 872
874→→¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑→→¬→𝜑¬𝜓𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜑] into ax-2
875→→¬→𝜑¬𝜓𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑Modus ponens 873, 874
876→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑Modus ponens 866, 875
877→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜓𝜒] into ax-2
878→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒Modus ponens 139, 877
879→→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒→¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒Subs [𝜑↗→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
880→¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒Modus ponens 878, 879
881→→¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜑, 𝜒↗→→𝜑→𝜓𝜒→𝜓𝜒] into ax-2
882→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒Modus ponens 880, 881
883→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒Modus ponens 876, 882
884→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
885→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
886→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒Modus ponens 884, 885
887→→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜑→𝜓𝜒] into ax-2
888→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒Modus ponens 886, 887
889→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
890→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒Modus ponens 883, 889
891→→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒Subs [𝜑↗→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
892→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒Modus ponens 890, 891
893→→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓→𝜑→𝜓𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜓𝜒] into ax-2
894→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒Modus ponens 892, 893
895→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒Modus ponens 884, 894
896→→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓Subs [𝜑↗→¬→𝜑¬𝜓𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1
897→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓Modus ponens simprim, 896
898→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒Subs [𝜑↗¬→𝜑¬𝜓] into ax-2
899→→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒Subs [𝜑↗→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
900→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒Modus ponens 898, 899
901→→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓→𝜓𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒] into ax-2
902→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒Modus ponens 900, 901
903→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒Modus ponens 895, 902
904→→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜓, 𝜒↗→¬→𝜑¬𝜓𝜒] into ax-2
905→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒Modus ponens 903, 904
906→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒Modus ponens 897, 905impt
907→→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬𝜑Subs [𝜑↗→¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
908→→𝜑¬𝜑→¬𝜑¬𝜑Modus ponens 310, 907
909→¬𝜑¬¬¬𝜑Subs [𝜑↗¬𝜑] into notnot
910→→¬𝜑¬¬¬𝜑→¬𝜑→¬𝜑¬¬¬𝜑Subs [𝜑↗→¬𝜑¬¬¬𝜑, 𝜓↗¬𝜑] into ax-1
911→¬𝜑→¬𝜑¬¬¬𝜑Modus ponens 909, 910
912→→¬𝜑→¬𝜑¬¬¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗¬¬¬𝜑] into ax-2
913→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑Modus ponens 911, 912
914→→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑Subs [𝜑↗→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
915→→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑Modus ponens 913, 914
916→→→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑→→→𝜑¬𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬¬¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬𝜑¬𝜑, 𝜒↗→¬𝜑¬¬¬𝜑] into ax-2
917→→→𝜑¬𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬¬¬𝜑Modus ponens 915, 916
918→→𝜑¬𝜑→¬𝜑¬¬¬𝜑Modus ponens 908, 917
919→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑Subs [𝜓↗¬¬𝜑] into ax-3
920→→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑Subs [𝜑↗→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
921→→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑Modus ponens 919, 920
922→→→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑→→→𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→¬¬𝜑𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬𝜑¬¬¬𝜑, 𝜒↗→¬¬𝜑𝜑] into ax-2
923→→→𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→¬¬𝜑𝜑Modus ponens 921, 922
924→→𝜑¬𝜑→¬¬𝜑𝜑Modus ponens 918, 923
925→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗¬¬𝜑] into ax-1
926→→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑Subs [𝜑↗→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
927→→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑Modus ponens 925, 926
928→→→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→¬¬𝜑→𝜑¬𝜑] into ax-2
929→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑Modus ponens 927, 928
930→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗¬𝜑] into ax-2
931→→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑Subs [𝜑↗→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
932→→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑Modus ponens 930, 931
933→→→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑→𝜑¬𝜑, 𝜒↗→→¬¬𝜑𝜑→¬¬𝜑¬𝜑] into ax-2
934→→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑Modus ponens 932, 933
935→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑Modus ponens 925, 934
936→→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→¬¬𝜑¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑𝜑, 𝜒↗→¬¬𝜑¬𝜑] into ax-2
937→→→𝜑¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→¬¬𝜑¬𝜑Modus ponens 935, 936
938→→𝜑¬𝜑→¬¬𝜑¬𝜑Modus ponens 924, 937
939→¬¬𝜑→¬𝜑¬→𝜑¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜑] into pm2.21
940→→¬¬𝜑→¬𝜑¬→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜑] into ax-2
941→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑Modus ponens 939, 940
942→→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑Subs [𝜑↗→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
943→→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑Modus ponens 941, 942
944→→→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑¬𝜑, 𝜒↗→¬¬𝜑¬→𝜑¬𝜑] into ax-2
945→→→𝜑¬𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑Modus ponens 943, 944
946→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑Modus ponens 938, 945
947→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-3
948→→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑Subs [𝜑↗→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
949→→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑Modus ponens 947, 948
950→→→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑¬→𝜑¬𝜑, 𝜒↗→→𝜑¬𝜑¬𝜑] into ax-2
951→→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑Modus ponens 949, 950
952→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑Modus ponens 946, 951
953→→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗¬𝜑] into ax-2
954→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑¬𝜑Modus ponens 952, 953
955→→𝜑¬𝜑¬𝜑Modus ponens 421, 954pm2.01
956→→¬𝜑𝜓→𝜓𝜓Subs [𝜑↗→¬𝜑𝜓] into idd
957→¬𝜑→→¬𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜑𝜓] into ax-1
958→→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑Subs [𝜑↗→¬𝜑→→¬𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
959→¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑Modus ponens 957, 958
960→→¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→→¬𝜑𝜓¬𝜑] into ax-2
961→→¬𝜑¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑Modus ponens 959, 960
962→→→¬𝜑𝜓→¬𝜑𝜓→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓Subs [𝜑↗→¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into ax-2
963→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓Modus ponens 447, 962
964→→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓→¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓Subs [𝜑↗→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓, 𝜓↗¬𝜑] into ax-1
965→¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓Modus ponens 963, 964
966→→¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓→→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→→¬𝜑𝜓𝜓Subs [𝜑↗¬𝜑, 𝜓↗→→¬𝜑𝜓¬𝜑, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
967→→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→→¬𝜑𝜓𝜓Modus ponens 965, 966
968→¬𝜑→→¬𝜑𝜓𝜓Modus ponens 957, 967
969→𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
970→→𝜓→→¬𝜑𝜓𝜓→𝜓→𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜓→→¬𝜑𝜓𝜓] into ax-1
971→𝜓→𝜓→→¬𝜑𝜓𝜓Modus ponens 969, 970
972→→𝜓→𝜓→→¬𝜑𝜓𝜓→→𝜓𝜓→𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
973→→𝜓𝜓→𝜓→→¬𝜑𝜓𝜓Modus ponens 971, 972
974→→→¬𝜑𝜓→𝜓𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→¬𝜑𝜓, 𝜒↗𝜓] into ax-2
975→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Modus ponens 956, 974
976→→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-1
977→𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Modus ponens 975, 976
978→→𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜓→→¬𝜑𝜓𝜓→𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
979→→𝜓→→¬𝜑𝜓𝜓→𝜓→→¬𝜑𝜓𝜓Modus ponens 977, 978
980→→𝜓→→¬𝜑𝜓𝜓→𝜑→𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜓→→¬𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
981→𝜑→𝜓→→¬𝜑𝜓𝜓Modus ponens 969, 980
982→→𝜑→𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓Subs [𝜒↗→→¬𝜑𝜓𝜓] into ax-2
983→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓Modus ponens 981, 982
984→→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓Subs [𝜑↗→¬𝜑→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
985→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓Modus ponens 968, 984
986→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓Subs [𝜑↗→→¬𝜑𝜓𝜓] into notnot
987→→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓→¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓Subs [𝜑↗→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓, 𝜓↗¬𝜑] into ax-1
988→¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓Modus ponens 986, 987
989→→¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓Subs [𝜑↗¬𝜑, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗¬¬→→¬𝜑𝜓𝜓] into ax-2
990→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓Modus ponens 988, 989
991→→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓Subs [𝜑↗→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
992→→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓Modus ponens 990, 991
993→→→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑→→¬𝜑𝜓𝜓, 𝜒↗→¬𝜑¬¬→→¬𝜑𝜓𝜓] into ax-2
994→→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓Modus ponens 992, 993
995→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓Modus ponens 985, 994
996→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑Subs [𝜓↗¬→→¬𝜑𝜓𝜓] into ax-3
997→→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑Subs [𝜑↗→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1
998→→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑Modus ponens 996, 997
999→→→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑→→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑¬¬→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓𝜑] into ax-2
1000→→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑Modus ponens 998, 999
1001→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑Modus ponens 995, 1000
1002→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜑→→¬𝜑𝜓𝜓, 𝜓↗¬→→¬𝜑𝜓𝜓] into ax-1
1003→→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓Subs [𝜑↗→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
1004→→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓Modus ponens 1002, 1003
1005→→→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓] into ax-2
1006→→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓Modus ponens 1004, 1005
1007→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓Modus ponens 983, 1006
1008→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗¬→→¬𝜑𝜓𝜓, 𝜓↗𝜑, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
1009→→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
1010→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Modus ponens 1008, 1009
1011→→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓, 𝜒↗→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-2
1012→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Modus ponens 1010, 1011
1013→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Modus ponens 1007, 1012
1014→→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓𝜑, 𝜒↗→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-2
1015→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Modus ponens 1013, 1014
1016→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓Modus ponens 1001, 1015
1017→¬→→¬𝜑𝜓𝜓→→→¬𝜑𝜓𝜓¬→𝜑𝜓Subs [𝜑↗→→¬𝜑𝜓𝜓, 𝜓↗¬→𝜑𝜓] into pm2.21
1018→→¬→→¬𝜑𝜓𝜓→→→¬𝜑𝜓𝜓¬→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓Subs [𝜑↗¬→→¬𝜑𝜓𝜓, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
1019→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓Modus ponens 1017, 1018
1020→→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1021→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓Modus ponens 1019, 1020
1022→→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓] into ax-2
1023→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓Modus ponens 1021, 1022
1024→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓Modus ponens 1016, 1023
1025→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-3
1026→→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
1027→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Modus ponens 1025, 1026
1028→→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→→¬𝜑𝜓𝜓] into ax-2
1029→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Modus ponens 1027, 1028
1030→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Modus ponens 1024, 1029
1031→→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
1032→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Modus ponens 1030, 1031
1033→→𝜑𝜓→→¬𝜑𝜓𝜓Modus ponens 24, 1032pm2.61
1034→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1035→→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓Subs [𝜑↗→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
1036→→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓Modus ponens 1034, 1035
1037→→→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗→→𝜑𝜓→¬𝜑𝜓] into ax-2
1038→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓Modus ponens 1036, 1037
1039→→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗𝜓] into ax-2
1040→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓Modus ponens pm2.61, 1039
1041→→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓→→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓Subs [𝜑↗→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
1042→→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓Modus ponens 1040, 1041
1043→→→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓→→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓𝜓Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→→𝜑𝜓→¬𝜑𝜓, 𝜒↗→→𝜑𝜓𝜓] into ax-2
1044→→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓𝜓Modus ponens 1042, 1043
1045→→¬𝜑𝜓→→𝜑𝜓𝜓Modus ponens 1034, 1044pm2.6
1046→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
1047→→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1048→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓Modus ponens 1046, 1047
1049→→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→¬𝜑𝜓→𝜑𝜓] into ax-2
1050→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓Modus ponens 1048, 1049
1051→→→¬𝜑𝜓→→𝜑𝜓𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2
1052→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓Modus ponens pm2.6, 1051
1053→→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
1054→→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓Modus ponens 1052, 1053
1055→→→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→→¬𝜑𝜓→𝜑𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
1056→→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓Modus ponens 1054, 1055
1057→→𝜑𝜓→¬𝜑¬𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑] into idd
1058→¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓] into ax-1
1059→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
1060→¬𝜑→¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1058, 1059
1061→→¬𝜑→¬𝜑→→𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1062→→¬𝜑¬𝜑→¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1060, 1061
1063→→→𝜑𝜓→¬𝜑¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜑] into ax-2
1064→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1057, 1063
1065→→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
1066→¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1064, 1065
1067→→¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1068→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1066, 1067
1069→¬𝜓→→𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗→𝜑𝜓] into ax-1
1070→→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→¬𝜓→→𝜑𝜓¬𝜓Subs [𝜑↗→¬𝜓→→𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
1071→¬𝜓→¬𝜓→→𝜑𝜓¬𝜓Modus ponens 1069, 1070
1072→→¬𝜓→¬𝜓→→𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→→𝜑𝜓¬𝜓] into ax-2
1073→→¬𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜓Modus ponens 1071, 1072
1074→→→𝜑𝜓→¬𝜓¬𝜑→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2
1075→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑Modus ponens con3, 1074
1076→→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑→¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑Subs [𝜑↗→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
1077→¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑Modus ponens 1075, 1076
1078→→¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑→→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→→𝜑𝜓¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1079→→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜑Modus ponens 1077, 1078
1080→¬𝜓→→𝜑𝜓¬𝜑Modus ponens 1069, 1079
1081→→¬𝜓→→𝜑𝜓¬𝜑→𝜑→¬𝜓→→𝜑𝜓¬𝜑Subs [𝜑↗→¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗𝜑] into ax-1
1082→𝜑→¬𝜓→→𝜑𝜓¬𝜑Modus ponens 1080, 1081
1083→→𝜑→¬𝜓→→𝜑𝜓¬𝜑→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑Subs [𝜓↗¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1084→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑Modus ponens 1082, 1083
1085→→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1086→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1058, 1085
1087→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑Subs [𝜑↗→→𝜑𝜓¬𝜑] into notnot
1088→→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑→¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑Subs [𝜑↗→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
1089→¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑Modus ponens 1087, 1088
1090→→¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗¬¬→→𝜑𝜓¬𝜑] into ax-2
1091→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑Modus ponens 1089, 1090
1092→→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑Subs [𝜑↗→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1093→→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑Modus ponens 1091, 1092
1094→→→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬𝜑¬¬→→𝜑𝜓¬𝜑] into ax-2
1095→→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑Modus ponens 1093, 1094
1096→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑Modus ponens 1086, 1095
1097→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑Subs [𝜓↗¬→→𝜑𝜓¬𝜑] into ax-3
1098→→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑Subs [𝜑↗→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1099→→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑Modus ponens 1097, 1098
1100→→→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑→→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑𝜑] into ax-2
1101→→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑Modus ponens 1099, 1100
1102→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑Modus ponens 1096, 1101
1103→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬→→𝜑𝜓¬𝜑] into ax-1
1104→→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1105→→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑Modus ponens 1103, 1104
1106→→→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑] into ax-2
1107→→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑Modus ponens 1105, 1106
1108→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑Modus ponens 1084, 1107
1109→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗¬→→𝜑𝜓¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1110→→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1111→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1109, 1110
1112→→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑, 𝜒↗→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑] into ax-2
1113→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1111, 1112
1114→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1108, 1113
1115→→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑] into ax-2
1116→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1114, 1115
1117→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑Modus ponens 1102, 1116
1118→¬→→𝜑𝜓¬𝜑→→→𝜑𝜓¬𝜑¬→𝜑¬𝜓Subs [𝜑↗→→𝜑𝜓¬𝜑, 𝜓↗¬→𝜑¬𝜓] into pm2.21
1119→→¬→→𝜑𝜓¬𝜑→→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓Subs [𝜑↗¬→→𝜑𝜓¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2
1120→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓Modus ponens 1118, 1119
1121→→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
1122→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓Modus ponens 1120, 1121
1123→→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓] into ax-2
1124→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓Modus ponens 1122, 1123
1125→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓Modus ponens 1117, 1124
1126→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑Subs [𝜑↗→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-3
1127→→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1128→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑Modus ponens 1126, 1127
1129→→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓→→𝜑𝜓¬𝜑] into ax-2
1130→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑Modus ponens 1128, 1129
1131→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑Modus ponens 1125, 1130
1132→→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1133→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑Modus ponens 1131, 1132
1134→→𝜑¬𝜓→→𝜑𝜓¬𝜑Modus ponens 379, 1133
1135→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
1136→→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1137→→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓Modus ponens 1135, 1136
1138→→→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑¬𝜓→𝜑𝜓] into ax-2
1139→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓Modus ponens 1137, 1138
1140→→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬𝜑] into ax-2
1141→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑Modus ponens 1134, 1140
1142→→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑→→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑Subs [𝜑↗→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑, 𝜓↗→𝜑𝜓] into ax-1
1143→→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑Modus ponens 1141, 1142
1144→→→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑→→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓¬𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑¬𝜓→𝜑𝜓, 𝜒↗→→𝜑¬𝜓¬𝜑] into ax-2
1145→→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓¬𝜑Modus ponens 1143, 1144
1146→→𝜑𝜓→→𝜑¬𝜓¬𝜑Modus ponens 1135, 1145pm2.65
1147→→𝜑𝜑→→𝜑𝜓→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜓] into ax-1
1148→→𝜑𝜓→𝜑𝜑Modus ponens id, 1147
1149→→→𝜑𝜓→𝜑𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2
1150→→→𝜑𝜓𝜑→→𝜑𝜓𝜑Modus ponens 1148, 1149
1151→→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑Subs [𝜑↗→¬→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1152→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑Modus ponens simplim, 1151
1153→→𝜑¬¬𝜑→¬→𝜑𝜓→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
1154→¬→𝜑𝜓→𝜑¬¬𝜑Modus ponens notnot, 1153
1155→→¬→𝜑𝜓→𝜑¬¬𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
1156→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑Modus ponens 1154, 1155
1157→→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑Subs [𝜑↗→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1158→→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑Modus ponens 1156, 1157
1159→→→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬→𝜑𝜓𝜑, 𝜒↗→¬→𝜑𝜓¬¬𝜑] into ax-2
1160→→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑Modus ponens 1158, 1159
1161→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑Modus ponens 1152, 1160
1162→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑] into ax-3
1163→→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓Subs [𝜑↗→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1164→→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓Modus ponens 1162, 1163
1165→→→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓→→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬→𝜑𝜓¬¬𝜑, 𝜒↗→¬𝜑→𝜑𝜓] into ax-2
1166→→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓Modus ponens 1164, 1165
1167→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓Modus ponens 1161, 1166
1168→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗¬𝜑] into ax-1
1169→→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑Subs [𝜑↗→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1170→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑Modus ponens 1168, 1169
1171→→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→¬𝜑→→𝜑𝜓𝜑] into ax-2
1172→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑Modus ponens 1170, 1171
1173→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗𝜑] into ax-2
1174→→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑Subs [𝜑↗→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1175→→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑Modus ponens 1173, 1174
1176→→→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑→→𝜑𝜓𝜑, 𝜒↗→→¬𝜑→𝜑𝜓→¬𝜑𝜑] into ax-2
1177→→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑Modus ponens 1175, 1176
1178→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑Modus ponens 1168, 1177
1179→→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→¬𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑→𝜑𝜓, 𝜒↗→¬𝜑𝜑] into ax-2
1180→→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→¬𝜑𝜑Modus ponens 1178, 1179
1181→→→𝜑𝜓𝜑→¬𝜑𝜑Modus ponens 1167, 1180
1182→¬𝜑→𝜑¬→→𝜑𝜓𝜑Subs [𝜓↗¬→→𝜑𝜓𝜑] into pm2.21
1183→→¬𝜑→𝜑¬→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗¬→→𝜑𝜓𝜑] into ax-2
1184→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑Modus ponens 1182, 1183
1185→→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑Subs [𝜑↗→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1186→→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑Modus ponens 1184, 1185
1187→→→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑→¬𝜑𝜑→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑¬→→𝜑𝜓𝜑] into ax-2
1188→→→→𝜑𝜓𝜑→¬𝜑𝜑→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑Modus ponens 1186, 1187
1189→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑Modus ponens 1181, 1188
1190→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑Subs [𝜓↗→→𝜑𝜓𝜑] into ax-3
1191→→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1192→→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑Modus ponens 1190, 1191
1193→→→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑¬→→𝜑𝜓𝜑, 𝜒↗→→→𝜑𝜓𝜑𝜑] into ax-2
1194→→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑Modus ponens 1192, 1193
1195→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑Modus ponens 1189, 1194
1196→→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗𝜑] into ax-2
1197→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑Modus ponens 1195, 1196
1198→→→𝜑𝜓𝜑𝜑Modus ponens 1150, 1197peirce
1199→→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜒↗𝜑] into imim1
1200→→→→𝜑𝜓𝜑𝜑→→𝜓𝜑→→→𝜑𝜓𝜑𝜑Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→𝜓𝜑] into ax-1
1201→→𝜓𝜑→→→𝜑𝜓𝜑𝜑Modus ponens peirce, 1200
1202→→→𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗𝜑] into ax-2
1203→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑Modus ponens 1201, 1202
1204→→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑→→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑Subs [𝜑↗→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜓] into ax-1
1205→→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑Modus ponens 1203, 1204
1206→→→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑→→→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜓→→𝜓𝜑𝜑Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→→𝜓𝜑→→𝜑𝜓𝜑, 𝜒↗→→𝜓𝜑𝜑] into ax-2
1207→→→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜓→→𝜓𝜑𝜑Modus ponens 1205, 1206
1208→→→𝜑𝜓𝜓→→𝜓𝜑𝜑Modus ponens 1199, 1207looinv
1209→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→𝜑𝜑] into pm2.01
1210→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1211→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Modus ponens id, 1210
1212→→𝜑𝜑→𝜑𝜑Subs [𝜑↗→𝜑𝜑] into id
1213→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1214→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1209, 1213
1215→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑] into notnotr
1216→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1217→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1218→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1216, 1217
1219→→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2
1220→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1218, 1219
1221→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1215, 1220
1222→→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2
1223→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1214, 1222
1224→→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1225→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1223, 1224
1226→→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬→𝜑𝜑] into ax-2
1227→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1225, 1226
1228→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1229→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Subs [𝜑↗→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1230→→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Modus ponens 1228, 1229
1231→→→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑] into ax-2
1232→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Modus ponens 1230, 1231
1233→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2
1234→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1215, 1233
1235→→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1236→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1234, 1235
1237→→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1238→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1236, 1237
1239→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1228, 1238
1240→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-3
1241→→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1242→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1240, 1241
1243→→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1244→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1242, 1243
1245→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1239, 1244
1246→→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1247→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1245, 1246
1248→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1212, 1247
1249→¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑] into id
1250→→¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1251→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1249, 1250
1252→¬¬¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑] into notnotr
1253→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1254→→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1
1255→¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1253, 1254
1256→→¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1257→→¬¬¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1255, 1256
1258→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1252, 1257
1259→→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2
1260→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1251, 1259
1261→→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1
1262→¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1260, 1261
1263→→¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1264→→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1262, 1263
1265→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑] into id
1266→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1
1267→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1268→→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1266, 1267
1269→→→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2
1270→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1268, 1269
1271→→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2
1272→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1258, 1271
1273→→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1274→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1272, 1273
1275→→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1276→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1274, 1275
1277→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1266, 1276
1278→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗¬¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-3
1279→→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1280→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1278, 1279
1281→→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬¬¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬¬→𝜑𝜑] into ax-2
1282→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1280, 1281
1283→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1277, 1282
1284→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2
1285→→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1283, 1284
1286→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1211, 1285
1287→→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1288→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1286, 1287
1289→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1290→→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1291→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1289, 1290
1292→→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2
1293→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1291, 1292
1294→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑Modus ponens 1215, 1293
1295→→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2
1296→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1288, 1295
1297→→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1298→¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1296, 1297
1299→→¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→𝜑𝜑] into ax-2
1300→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1298, 1299
1301→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1294, 1300
1302→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1303→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1304→¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1302, 1303
1305→→¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1306→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1304, 1305
1307→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2
1308→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1301, 1307
1309→→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1310→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1308, 1309
1311→→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑] into ax-2
1312→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1310, 1311
1313→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑Modus ponens 1302, 1312
1314→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-3
1315→→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1316→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1314, 1315
1317→→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1318→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1316, 1317
1319→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1313, 1318
1320→→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1321→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1319, 1320
1322→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1249, 1321
1323→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑] into id
1324→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1325→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1323, 1324
1326→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑] into notnotr
1327→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1328→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1329→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1327, 1328
1330→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1331→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1329, 1330
1332→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1326, 1331
1333→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1334→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1325, 1333
1335→→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1336→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1334, 1335
1337→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1338→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1336, 1337
1339→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1340→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1341→¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1339, 1340
1342→→¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1343→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑Modus ponens 1341, 1342
1344→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1345→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1332, 1344
1346→→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1347→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1345, 1346
1348→→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1349→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1347, 1348
1350→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1339, 1349
1351→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-3
1352→→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1353→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1351, 1352
1354→→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1355→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1353, 1354
1356→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1350, 1355
1357→→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1358→→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1356, 1357
1359→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1322, 1358
1360→→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-3
1361→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑Modus ponens 1359, 1360
1362→→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1363→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1248, 1362
1364→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1365→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1363, 1364
1366→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1361, 1365
1367→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑] into pm2.18
1368¬→→𝜑𝜑¬→𝜑𝜑Modus ponens 1366, 1367bijust0
1369¬→→¬→→𝜑𝜓¬→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑] into bijust0bijust
1370→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into simprim
1371→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens df-bi, 1370
1372→→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into pm3.2im
1373→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1
1374→→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1371, 1373
1375→→→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
1376→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓Modus ponens 1374, 1375
1377→→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1378→→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓Modus ponens 1376, 1377
1379→→→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→→→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→𝜓𝜑↔𝜑𝜓] into ax-2
1380→→→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓Modus ponens 1378, 1379
1381→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓Modus ponens 1372, 1380impbi
1382→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into impbi
1383→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into notnotr
1384→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1385→→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1386→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1384, 1385
1387→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1388→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1386, 1387
1389→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1383, 1388
1390→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1391→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1382, 1390
1392→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1393→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1391, 1392
1394→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1395→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1393, 1394
1396→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1389, 1395
1397→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id
1398→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1399→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1400→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1398, 1399
1401→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1402→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1400, 1401
1403→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1404→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1396, 1403
1405→→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1406→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1404, 1405
1407→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1408→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1406, 1407
1409→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1398, 1408
1410→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnot
1411→→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1412→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1410, 1411
1413→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1414→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1412, 1413
1415→→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1416→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1414, 1415
1417→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1418→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1416, 1417
1419→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1409, 1418
1420→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1421→→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1422→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1420, 1421
1423→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1424→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1422, 1423
1425→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1419, 1424
1426→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id
1427→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1428→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1429→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1427, 1428
1430→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1431→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1429, 1430
1432→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1433→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1425, 1432
1434→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1435→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1433, 1434
1436→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1437→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1435, 1436
1438→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1427, 1437
1439→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1440→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens df-bi, 1439
1441→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into id
1442→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1443→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1440, 1442
1444→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnotr
1445→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1446→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1447→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1445, 1446
1448→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1449→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1447, 1448
1450→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1444, 1449
1451→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1452→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1443, 1451
1453→→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1454→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1452, 1453
1455→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1456→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1454, 1455
1457→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1450, 1456
1458→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1459→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1460→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1458, 1459
1461→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1462→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1460, 1461
1463→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1464→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1457, 1463
1465→→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1466→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1464, 1465
1467→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1468→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1466, 1467
1469→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1458, 1468
1470→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3
1471→→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1472→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1470, 1471
1473→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1474→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1472, 1473
1475→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1469, 1474
1476→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1477→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1475, 1476
1478→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1441, 1477
1479→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into id
1480→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1481→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1479, 1480
1482→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into notnotr
1483→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1484→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1439, 1483
1485→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1486→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1484, 1485
1487→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1482, 1486
1488→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1489→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1481, 1488
1490→→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1491→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1489, 1490
1492→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1493→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1491, 1492
1494→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1495→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1496→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1494, 1495
1497→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1498→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1496, 1497
1499→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1500→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1487, 1499
1501→→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1502→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1500, 1501
1503→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1504→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1502, 1503
1505→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1494, 1504
1506→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3
1507→→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1508→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1506, 1507
1509→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1510→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1508, 1509
1511→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1505, 1510
1512→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1513→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1511, 1512
1514→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1438, 1513
1515→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1516→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1514, 1515
1517→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1518→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1519→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1517, 1518
1520→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1521→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1519, 1520
1522→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1444, 1521
1523→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1524→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1516, 1523
1525→→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1526→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1524, 1525
1527→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1528→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1526, 1527
1529→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1522, 1528
1530→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1531→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1532→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1530, 1531
1533→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1534→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1532, 1533
1535→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1536→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1529, 1535
1537→→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1538→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1536, 1537
1539→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1540→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1538, 1539
1541→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1530, 1540
1542→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3
1543→→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1544→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1542, 1543
1545→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1546→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1544, 1545
1547→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1541, 1546
1548→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1549→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1547, 1548
1550→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1479, 1549
1551→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id
1552→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1553→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1551, 1552
1554→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnotr
1555→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1556→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1557→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1555, 1556
1558→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1559→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1557, 1558
1560→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1554, 1559
1561→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1562→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1553, 1561
1563→→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1564→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1562, 1563
1565→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1566→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1564, 1565
1567→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1568→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1569→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1567, 1568
1570→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1571→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1569, 1570
1572→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1573→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1560, 1572
1574→→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1575→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1573, 1574
1576→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1577→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1575, 1576
1578→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1567, 1577
1579→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1580→→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1581→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1579, 1580
1582→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1583→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1581, 1582
1584→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1578, 1583
1585→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1586→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1584, 1585
1587→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1550, 1586
1588→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1589→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1587, 1588
1590→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1591→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1478, 1590
1592→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1593→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1591, 1592
1594→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1589, 1593
1595→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into pm2.18
1596¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1594, 1595
1597→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1598→¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1596, 1597
1599→→¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1600→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1598, 1599
1601→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1602→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1600, 1601
1603↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 1596, 1602dfbi1
1604→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into simplim
1605→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Modus ponens df-bi, 1604
1606→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜓𝜑] into simplim
1607→→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1608→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓Modus ponens 1606, 1607
1609→→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2
1610→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜑𝜓Modus ponens 1608, 1609
1611→↔𝜑𝜓→𝜑𝜓Modus ponens 1605, 1610biimp
1612→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into simprim
1613→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into biimp
1614→→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1615→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑Modus ponens 1612, 1614
1616→→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2
1617→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜓𝜑Modus ponens 1615, 1616
1618→↔𝜑𝜓→𝜓𝜑Modus ponens 1605, 1617biimpr
1619→→𝜓𝜑→→𝜑𝜓↔𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗𝜑] into impbi
1620→→𝜑𝜓→→𝜓𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1
1621→→→𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜓𝜑→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1622→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓Modus ponens 1620, 1621
1623→→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜑→𝜑𝜓] into ax-2
1624→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓Modus ponens 1622, 1623
1625→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓Modus ponens biimp, 1624
1626→→→𝜓𝜑→→𝜑𝜓↔𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2
1627→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑Modus ponens 1619, 1626
1628→→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑→↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑Subs [𝜑↗→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1629→↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑Modus ponens 1627, 1628
1630→→↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑→→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜑→𝜑𝜓, 𝜒↗→→𝜓𝜑↔𝜓𝜑] into ax-2
1631→→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑Modus ponens 1629, 1630
1632→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑Modus ponens 1625, 1631
1633→→𝜓𝜑→𝜓𝜑Subs [𝜑↗→𝜓𝜑] into id
1634→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1635→→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑Subs [𝜑↗→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1
1636→→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑Modus ponens 1634, 1635
1637→→→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→↔𝜑𝜓→𝜓𝜑] into ax-2
1638→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑Modus ponens 1636, 1637
1639→→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜓𝜑] into ax-2
1640→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Modus ponens 1632, 1639
1641→→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1
1642→→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Modus ponens 1640, 1641
1643→→→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗→↔𝜑𝜓→𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2
1644→→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Modus ponens 1642, 1643
1645→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Modus ponens 1634, 1644
1646→→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1647→↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Modus ponens 1645, 1646
1648→→↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2
1649→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Modus ponens 1647, 1648
1650→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Modus ponens biimpr, 1649
1651→↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓] into id
1652→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1653→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1654→↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓Modus ponens 1652, 1653
1655→→↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜓] into ax-2
1656→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓Modus ponens 1654, 1655
1657→→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2
1658→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Modus ponens 1650, 1657
1659→→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1660→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Modus ponens 1658, 1659
1661→→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2
1662→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Modus ponens 1660, 1661
1663→↔𝜑𝜓↔𝜓𝜑Modus ponens 1651, 1658bicom1
1664→↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into bicom1
1665→→↔𝜑𝜓↔𝜓𝜑→→↔𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into impbi
1666→→↔𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑Modus ponens bicom1, 1665
1667↔↔𝜑𝜓↔𝜓𝜑Modus ponens 1664, 1666bicom
1668→→𝜑𝜑→→𝜑𝜑↔𝜑𝜑Subs [𝜓↗𝜑] into impbi
1669→→𝜑𝜑↔𝜑𝜑Modus ponens id, 1668
1670↔𝜑𝜑Modus ponens id, 1669biid
1671↔𝜓𝜓Subs [𝜑↗𝜓] into biid
1672→↔𝜓𝜓→𝜑↔𝜓𝜓Subs [𝜑↗↔𝜓𝜓, 𝜓↗𝜑] into ax-1
1673→𝜑↔𝜓𝜓Modus ponens 1671, 1672biidd
1674→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1
1675→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗𝜑] into ax-1
1676→𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Modus ponens 1674, 1675
1677→→𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜑→𝜓𝜑→𝜑→→𝜑𝜓→𝜓𝜑Subs [𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2
1678→→𝜑→𝜓𝜑→𝜑→→𝜑𝜓→𝜓𝜑Modus ponens 1676, 1677
1679→𝜑→→𝜑𝜓→𝜓𝜑Modus ponens ax-1, 1678
1680→→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
1681→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Modus ponens impbi, 1680
1682→→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
1683→𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Modus ponens 1681, 1682
1684→→𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜑𝜓↔𝜑𝜓Subs [𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2
1685→→𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜑𝜓↔𝜑𝜓Modus ponens 1683, 1684
1686→𝜑→→𝜑𝜓↔𝜑𝜓Modus ponens 1679, 1685
1687→→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1688→→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓Modus ponens 533, 1687
1689→→→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into ax-2
1690→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓Modus ponens 1688, 1689
1691→→𝜑→→𝜑𝜓↔𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2
1692→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 1686, 1691
1693→→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1694→→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 1692, 1693
1695→→→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓→→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2
1696→→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 1694, 1695
1697→→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 533, 1696
1698→→→𝜑𝜓→𝜑↔𝜑𝜓→𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓] into ax-1
1699→𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 1697, 1698
1700→→𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜑↔𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2
1701→→𝜓→𝜑𝜓→𝜓→𝜑↔𝜑𝜓Modus ponens 1699, 1700
1702→𝜓→𝜑↔𝜑𝜓Modus ponens 208, 1701
1703→→𝜑→𝜓𝜑→𝜑→𝜑→𝜓𝜑Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗𝜑] into ax-1
1704→𝜑→𝜑→𝜓𝜑Modus ponens ax-1, 1703
1705→→𝜑→𝜑→𝜓𝜑→→𝜑𝜑→𝜑→𝜓𝜑Subs [𝜓↗𝜑, 𝜒↗→𝜓𝜑] into ax-2
1706→→𝜑𝜑→𝜑→𝜓𝜑Modus ponens 1704, 1705
1707→→𝜓→𝜑↔𝜑𝜓→→𝜓𝜑→𝜓↔𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗↔𝜑𝜓] into ax-2
1708→→𝜓𝜑→𝜓↔𝜑𝜓Modus ponens 1702, 1707
1709→→→𝜓𝜑→𝜓↔𝜑𝜓→𝜑→→𝜓𝜑→𝜓↔𝜑𝜓Subs [𝜑↗→→𝜓𝜑→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
1710→𝜑→→𝜓𝜑→𝜓↔𝜑𝜓Modus ponens 1708, 1709
1711→→𝜑→→𝜓𝜑→𝜓↔𝜑𝜓→→𝜑→𝜓𝜑→𝜑→𝜓↔𝜑𝜓Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓↔𝜑𝜓] into ax-2
1712→→𝜑→𝜓𝜑→𝜑→𝜓↔𝜑𝜓Modus ponens 1710, 1711
1713→𝜑→𝜓↔𝜑𝜓Modus ponens ax-1, 1712pm5.1im
1714→→𝜓𝜓→→𝜑𝜑→𝜓𝜓Subs [𝜑↗→𝜓𝜓, 𝜓↗→𝜑𝜑] into ax-1
1715→→𝜑𝜑→𝜓𝜓Modus ponens 10, 1714
1716→→𝜑𝜑→→𝜓𝜓→𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜓𝜓] into ax-1
1717→→𝜓𝜓→𝜑𝜑Modus ponens id, 1716
1718→→→𝜑𝜑→𝜓𝜓→→→𝜓𝜓→𝜑𝜑↔→𝜑𝜑→𝜓𝜓Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜓𝜓] into impbi
1719→→→𝜓𝜓→𝜑𝜑↔→𝜑𝜑→𝜓𝜓Modus ponens 1715, 1718
1720↔→𝜑𝜑→𝜓𝜓Modus ponens 1717, 1719monothetic
1721→↔𝜓𝜒→𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into biimp
1722→→↔𝜓𝜒→𝜓𝜒→𝜑→↔𝜓𝜒→𝜓𝜒Subs [𝜑↗→↔𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
1723→𝜑→↔𝜓𝜒→𝜓𝜒Modus ponens 1721, 1722
1724→→𝜑→↔𝜓𝜒→𝜓𝜒→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒Subs [𝜓↗↔𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
1725→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒Modus ponens 1723, 1724
1726→→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1727→→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens ax-2, 1726
1728→→→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
1729→→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 1727, 1728
1730→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 1725, 1729
1731→↔𝜓𝜒→𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗𝜒] into biimpr
1732→→↔𝜓𝜒→𝜒𝜓→𝜑→↔𝜓𝜒→𝜒𝜓Subs [𝜑↗→↔𝜓𝜒→𝜒𝜓, 𝜓↗𝜑] into ax-1
1733→𝜑→↔𝜓𝜒→𝜒𝜓Modus ponens 1731, 1732
1734→→𝜑→↔𝜓𝜒→𝜒𝜓→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓Subs [𝜓↗↔𝜓𝜒, 𝜒↗→𝜒𝜓] into ax-2
1735→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓Modus ponens 1733, 1734
1736→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓Subs [𝜓↗𝜒, 𝜒↗𝜓] into ax-2
1737→→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1738→→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓Modus ponens 1736, 1737
1739→→→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑→𝜒𝜓, 𝜒↗→→𝜑𝜒→𝜑𝜓] into ax-2
1740→→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓Modus ponens 1738, 1739
1741→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓Modus ponens 1735, 1740
1742→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into impbi
1743→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜒→𝜑𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
1744→→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1745→→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓Modus ponens 1743, 1744
1746→→→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓] into ax-2
1747→→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓Modus ponens 1745, 1746
1748→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓Modus ponens 1741, 1747
1749→→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2
1750→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1742, 1749
1751→→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1752→→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1750, 1751
1753→→→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1754→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1752, 1753
1755→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1748, 1754
1756→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1757→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
1758→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 1756, 1757
1759→→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2
1760→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 1758, 1759
1761→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2
1762→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1755, 1761
1763→→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
1764→→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1762, 1763
1765→→→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1766→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1764, 1765
1767→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1756, 1766
1768→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1769→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1767, 1768
1770→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1771→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1769, 1770
1772→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1730, 1771
1773→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒] into id
1774→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1775→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1776→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 1774, 1775
1777→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒] into ax-2
1778→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 1776, 1777
1779→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2
1780→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1772, 1779
1781→→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1782→→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1780, 1781
1783→→→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1784→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1782, 1783
1785→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1773, 1780
1786→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into biimp
1787→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1788→→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-1
1789→𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 1787, 1788
1790→→𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2
1791→→𝜓→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 1789, 1790
1792→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 208, 1791
1793→→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
1794→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 1786, 1793
1795→→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-1
1796→𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 1794, 1795
1797→→𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2
1798→→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 1796, 1797
1799→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 1792, 1798
1800→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒] into id
1801→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1802→→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1803→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒Modus ponens 1801, 1802
1804→→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓↔→𝜑𝜓→𝜑𝜒] into ax-2
1805→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒Modus ponens 1803, 1804
1806→→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜒] into ax-2
1807→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Modus ponens 1799, 1806
1808→→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Subs [𝜑↗→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1809→↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Modus ponens 1807, 1808
1810→→↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2
1811→→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Modus ponens 1809, 1810
1812→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒Modus ponens 1801, 1811
1813→→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒Subs [𝜑↗→𝜑→→𝜑𝜒𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1814→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒Modus ponens 264, 1813
1815→→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Subs [𝜑↗→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1816→↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Modus ponens 267, 1815
1817→→↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓→𝜑𝜒] into ax-2
1818→→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Modus ponens 1816, 1817
1819→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒Modus ponens 1812, 1818
1820→→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1821→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Modus ponens 277, 1820
1822→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2
1823→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Modus ponens 1821, 1822
1824→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒Modus ponens 1814, 1823
1825→→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1826→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 283, 1825
1827→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜒↗→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒] into ax-2
1828→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 1826, 1827
1829→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 1824, 1828
1830→→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
1831→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 1829, 1830
1832→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens 1819, 1831
1833→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into biimpr
1834→𝜒→𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗𝜑] into ax-1
1835→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1836→→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒, 𝜓↗𝜒] into ax-1
1837→𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 1835, 1836
1838→→𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2
1839→→𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 1837, 1838
1840→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒Modus ponens 1834, 1839
1841→→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into ax-2
1842→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 1833, 1841
1843→→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜓↗𝜒] into ax-1
1844→𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 1842, 1843
1845→→𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2
1846→→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 1844, 1845
1847→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓Modus ponens 1840, 1846
1848→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗𝜒] into ax-1
1849→→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1850→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1848, 1849
1851→→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1852→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1850, 1851
1853→→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜓] into ax-2
1854→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓Modus ponens 1847, 1853
1855→→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓Subs [𝜑↗→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1856→↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓Modus ponens 1854, 1855
1857→→↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜒↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜒→𝜑𝜓] into ax-2
1858→→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓Modus ponens 1856, 1857
1859→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓Modus ponens 1848, 1858
1860→→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓Subs [𝜑↗→𝜑→→𝜑𝜓𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1861→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓Modus ponens pm2.27, 1860
1862→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓Subs [𝜑↗→𝜒→𝜑𝜓, 𝜓↗𝜑] into ax-1
1863→→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓Subs [𝜑↗→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1864→↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓Modus ponens 1862, 1863
1865→→↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜑→𝜒→𝜑𝜓] into ax-2
1866→→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓Modus ponens 1864, 1865
1867→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓Modus ponens 1859, 1866
1868→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓Subs [𝜑↗→𝜑𝜓] into imim2
1869→→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓→𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓Subs [𝜑↗→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓, 𝜓↗𝜑] into ax-1
1870→𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓Modus ponens 1868, 1869
1871→→𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗→→𝜒→𝜑𝜓→𝜒𝜓] into ax-2
1872→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓Modus ponens 1870, 1871
1873→→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓Subs [𝜑↗→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1874→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓Modus ponens 1872, 1873
1875→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜓𝜓, 𝜒↗→𝜑→→𝜒→𝜑𝜓→𝜒𝜓] into ax-2
1876→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓Modus ponens 1874, 1875
1877→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓Modus ponens 1861, 1876
1878→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓Subs [𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2
1879→→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓Subs [𝜑↗→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1880→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓Modus ponens 1878, 1879
1881→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜒→𝜑𝜓→𝜒𝜓, 𝜒↗→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓] into ax-2
1882→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓Modus ponens 1880, 1881
1883→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓Modus ponens 1877, 1882
1884→→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜒→𝜑𝜓, 𝜒↗→𝜑→𝜒𝜓] into ax-2
1885→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓Modus ponens 1883, 1884
1886→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓Modus ponens 1867, 1885
1887→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into impbi
1888→→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒→𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒Subs [𝜑↗→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒, 𝜓↗𝜑] into ax-1
1889→𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒Modus ponens 1887, 1888
1890→→𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒Subs [𝜓↗→𝜓𝜒, 𝜒↗→→𝜒𝜓↔𝜓𝜒] into ax-2
1891→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒Modus ponens 1889, 1890
1892→→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒Subs [𝜑↗→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1893→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒Modus ponens 1891, 1892
1894→→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜑→→𝜒𝜓↔𝜓𝜒] into ax-2
1895→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒Modus ponens 1893, 1894
1896→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒Modus ponens 1832, 1895
1897→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒Subs [𝜓↗→𝜒𝜓, 𝜒↗↔𝜓𝜒] into ax-2
1898→→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒Subs [𝜑↗→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1899→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒Modus ponens 1897, 1898
1900→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜒𝜓↔𝜓𝜒, 𝜒↗→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒] into ax-2
1901→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒Modus ponens 1899, 1900
1902→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒Modus ponens 1896, 1901
1903→→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜒𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
1904→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Modus ponens 1902, 1903
1905→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Modus ponens 1886, 1904
1906→→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into impbi
1907→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1785, 1906
1908↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 1905, 1907pm5.74
1909→→𝜑¬¬𝜑→→¬¬𝜑𝜑↔𝜑¬¬𝜑Subs [𝜓↗¬¬𝜑] into impbi
1910→→¬¬𝜑𝜑↔𝜑¬¬𝜑Modus ponens notnot, 1909
1911↔𝜑¬¬𝜑Modus ponens notnotr, 1910notnotb
1912→→→𝜑𝜓→¬𝜓¬𝜑→→→¬𝜓¬𝜑→𝜑𝜓↔→𝜑𝜓→¬𝜓¬𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜓¬𝜑] into impbi
1913→→→¬𝜓¬𝜑→𝜑𝜓↔→𝜑𝜓→¬𝜓¬𝜑Modus ponens con3, 1912
1914↔→𝜑𝜓→¬𝜓¬𝜑Modus ponens 316, 1913con34b
1915↔𝜓¬¬𝜓Subs [𝜑↗𝜓] into notnotb
1916→↔𝜑¬¬𝜑↔¬¬𝜑𝜑Subs [𝜓↗¬¬𝜑] into bicom1
1917↔¬¬𝜑𝜑Modus ponens notnotb, 1916
1918→↔¬¬𝜑𝜑→↔𝜑𝜓↔¬¬𝜑𝜑Subs [𝜑↗↔¬¬𝜑𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1919→↔𝜑𝜓↔¬¬𝜑𝜑Modus ponens 1917, 1918
1920↔→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗𝜑] into pm5.74
1921→↔→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜑, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑] into biimp
1922→→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑Modus ponens 1920, 1921
1923↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑Modus ponens 1919, 1922
1924↔→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74
1925→↔→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp
1926→→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 1924, 1925
1927↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 1651, 1926
1928→↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜓] into biimp
1929→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 1927, 1928
1930→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑] into biimp
1931→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑Modus ponens 1923, 1930
1932→→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into ax-1
1933→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 1929, 1932
1934→→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into ax-2
1935→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Modus ponens 1933, 1934
1936→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Modus ponens 1931, 1935
1937→↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜓] into bicom1
1938↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 1927, 1937
1939→↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜑] into biimp
1940→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 1938, 1939
1941→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑] into bicom1
1942↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑Modus ponens 1923, 1941
1943→↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜑] into biimp
1944→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑Modus ponens 1942, 1943
1945→→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into ax-1
1946→→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑Modus ponens 1944, 1945
1947→→→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2
1948→→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 1946, 1947
1949→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 1940, 1948
1950→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into impbi
1951→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Modus ponens 1936, 1950
1952↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Modus ponens 1949, 1951
1953↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗𝜓] into pm5.74
1954→↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓] into bicom1
1955↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓Modus ponens 1953, 1954
1956→↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓Subs [𝜑↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔¬¬𝜑𝜓] into biimp
1957→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓Modus ponens 1955, 1956
1958→↔𝜑𝜓↔¬¬𝜑𝜓Modus ponens 1952, 1957
1959→↔𝜓¬¬𝜓→↔𝜑𝜓↔𝜓¬¬𝜓Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1960→↔𝜑𝜓↔𝜓¬¬𝜓Modus ponens 1915, 1959
1961→↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓] into biimp
1962→→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Modus ponens 1953, 1961
1963↔→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74
1964→↔→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜓¬¬𝜓, 𝜓↗↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓] into biimp
1965→→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓Modus ponens 1963, 1964
1966↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓Modus ponens 1960, 1965
1967→↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓] into biimp
1968→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓Modus ponens 1966, 1967
1969→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into biimp
1970→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into ax-1
1971→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓Modus ponens 1968, 1970
1972→→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜓] into ax-2
1973→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓Modus ponens 1971, 1972
1974→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓Modus ponens 1936, 1973
1975→↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓] into bicom1
1976↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓Modus ponens 1966, 1975
1977→↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓𝜓] into biimp
1978→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓Modus ponens 1976, 1977
1979→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into bicom1
1980↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 1952, 1979
1981→↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into biimp
1982→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜓] into ax-1
1983→→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 1949, 1982
1984→→→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2
1985→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 1983, 1984
1986→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 1978, 1985
1987→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜓] into impbi
1988→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓Modus ponens 1974, 1987
1989↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓Modus ponens 1986, 1988
1990↔→↔𝜑𝜓↔¬¬𝜑¬¬𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗¬¬𝜓] into pm5.74
1991→↔→↔𝜑𝜓↔¬¬𝜑¬¬𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑¬¬𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓] into bicom1
1992↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓Modus ponens 1990, 1991
1993→↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓Subs [𝜑↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓↔¬¬𝜑¬¬𝜓] into biimp
1994→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓Modus ponens 1992, 1993
1995→↔𝜑𝜓↔¬¬𝜑¬¬𝜓Modus ponens 1989, 1994
1996→¬¬𝜓¬¬𝜓Subs [𝜑↗¬¬𝜓] into id
1997↔↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗¬¬𝜓] into bicom
1998→↔↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑Subs [𝜑↗↔¬¬𝜑¬¬𝜓, 𝜓↗↔¬¬𝜓¬¬𝜑] into biimp
1999→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑Modus ponens 1997, 1998
2000→→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑Subs [𝜑↗→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2001→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑Modus ponens 1999, 2000
2002→→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓↔¬¬𝜓¬¬𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜑¬¬𝜓, 𝜒↗↔¬¬𝜓¬¬𝜑] into ax-2
2003→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓↔¬¬𝜓¬¬𝜑Modus ponens 2001, 2002
2004→↔𝜑𝜓↔¬¬𝜓¬¬𝜑Modus ponens 1995, 2003
2005→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜑] into biimp
2006→→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑→↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑Subs [𝜑↗→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2007→↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑Modus ponens 2005, 2006
2008→→↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑→→↔𝜑𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬¬𝜓¬¬𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜓¬¬𝜑, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2
2009→→↔𝜑𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬¬𝜓¬¬𝜑Modus ponens 2007, 2008
2010→↔𝜑𝜓→¬¬𝜓¬¬𝜑Modus ponens 2004, 2009
2011→¬¬𝜓→↔𝜑𝜓¬¬𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2012→→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓Subs [𝜑↗→¬¬𝜓→↔𝜑𝜓¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1
2013→¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓Modus ponens 2011, 2012
2014→→¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓→→¬¬𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜓] into ax-2
2015→→¬¬𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓Modus ponens 2013, 2014
2016→→↔𝜑𝜓→¬¬𝜓¬¬𝜑→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜓, 𝜒↗¬¬𝜑] into ax-2
2017→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑→¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑Subs [𝜑↗→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑, 𝜓↗¬¬𝜓] into ax-1
2018→¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 1986, 2017
2019→→¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑→→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2
2020→→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 2018, 2019
2021→¬¬𝜓→↔𝜑𝜓¬¬𝜑Modus ponens 2011, 2020
2022→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
2023→→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2024→↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓Modus ponens 2022, 2023
2025→→↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬𝜓↔𝜑𝜓] into ax-2
2026→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓Modus ponens 2024, 2025
2027→→¬¬𝜓→↔𝜑𝜓¬¬𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬𝜑] into ax-2
2028→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑Modus ponens 2021, 2027
2029→→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑Subs [𝜑↗→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2030→↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑Modus ponens 2028, 2029
2031→→↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑→→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓¬¬𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2
2032→→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓¬¬𝜑Modus ponens 2030, 2031
2033→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into ax-3
2034→→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2035→↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓Modus ponens 2033, 2034
2036→→↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→→↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜓¬¬𝜑, 𝜒↗→¬𝜑¬𝜓] into ax-2
2037→→↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 2035, 2036
2038→↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 2010, 2037
2039→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗¬¬𝜑, 𝜓↗¬¬𝜓] into biimp
2040→→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2041→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓Modus ponens 2039, 2040
2042→→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜑¬¬𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2
2043→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬¬𝜑¬¬𝜓Modus ponens 2041, 2042
2044→↔𝜑𝜓→¬¬𝜑¬¬𝜓Modus ponens 1995, 2043
2045→→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2046→↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Modus ponens 494, 2045
2047→→↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→↔𝜑𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬𝜓¬𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
2048→→↔𝜑𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬𝜓¬𝜑Modus ponens 2046, 2047
2049→↔𝜑𝜓→¬𝜓¬𝜑Modus ponens 2044, 2048
2050→→¬𝜑¬𝜓→→¬𝜓¬𝜑↔¬𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into impbi
2051→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜑¬𝜓] into ax-1
2052→→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑Subs [𝜑↗→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2053→↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑Modus ponens 2051, 2052
2054→→↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑→→↔𝜑𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→→¬𝜑¬𝜓→¬𝜓¬𝜑] into ax-2
2055→→↔𝜑𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑Modus ponens 2053, 2054
2056→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑Modus ponens 2049, 2055
2057→→→¬𝜑¬𝜓→→¬𝜓¬𝜑↔¬𝜑¬𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗↔¬𝜑¬𝜓] into ax-2
2058→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓Modus ponens 2050, 2057
2059→→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2060→↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓Modus ponens 2058, 2059
2061→→↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜒↗→→¬𝜑¬𝜓↔¬𝜑¬𝜓] into ax-2
2062→→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓Modus ponens 2060, 2061
2063→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓Modus ponens 2056, 2062
2064→→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓] into id
2065→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2066→→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1
2067→→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 2065, 2066
2068→→→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓→¬𝜑¬𝜓] into ax-2
2069→→→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 2067, 2068
2070→→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗↔¬𝜑¬𝜓] into ax-2
2071→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2063, 2070
2072→→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1
2073→→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2071, 2072
2074→→→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→↔𝜑𝜓→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2
2075→→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2073, 2074
2076→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2065, 2075
2077→→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2078→↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2076, 2077
2079→→↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2
2080→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2078, 2079
2081→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2038, 2080
2082→→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔¬𝜑¬𝜓] into ax-2
2083→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2081, 2082
2084→→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2085→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2083, 2084
2086→→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2
2087→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2085, 2086
2088→↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 1651, 2083
2089→↔¬𝜑¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔¬𝜑¬𝜓] into id
2090↔↔¬𝜑¬𝜓↔¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into bicom
2091→↔↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓↔¬𝜓¬𝜑Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜓¬𝜑] into biimp
2092→↔¬𝜑¬𝜓↔¬𝜓¬𝜑Modus ponens 2090, 2091
2093→→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑Subs [𝜑↗→↔¬𝜑¬𝜓↔¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2094→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑Modus ponens 2092, 2093
2095→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔¬𝜓¬𝜑] into ax-2
2096→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑Modus ponens 2094, 2095
2097→↔¬𝜓¬𝜑→¬𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into biimp
2098→→↔¬𝜓¬𝜑→¬𝜓¬𝜑→↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑Subs [𝜑↗→↔¬𝜓¬𝜑→¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2099→↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑Modus ponens 2097, 2098
2100→→↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑→→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→¬𝜓¬𝜑Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜓¬𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2
2101→→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→¬𝜓¬𝜑Modus ponens 2099, 2100
2102→↔¬𝜑¬𝜓→¬𝜓¬𝜑Modus ponens 2092, 2101
2103→¬𝜓→↔¬𝜑¬𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2104→→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓Subs [𝜑↗→¬𝜓→↔¬𝜑¬𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
2105→¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓Modus ponens 2103, 2104
2106→→¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→↔¬𝜑¬𝜓¬𝜓] into ax-2
2107→→¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓Modus ponens 2105, 2106
2108→→↔¬𝜑¬𝜓→¬𝜓¬𝜑→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2
2109→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑Modus ponens 2102, 2108
2110→→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑→¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑Subs [𝜑↗→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
2111→¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑Modus ponens 2109, 2110
2112→→¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑→→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→↔¬𝜑¬𝜓¬𝜓, 𝜒↗→↔¬𝜑¬𝜓¬𝜑] into ax-2
2113→→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜑Modus ponens 2111, 2112
2114→¬𝜓→↔¬𝜑¬𝜓¬𝜑Modus ponens 2103, 2113
2115→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
2116→→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2117→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓Modus ponens 2115, 2116
2118→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→¬𝜓↔¬𝜑¬𝜓] into ax-2
2119→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓Modus ponens 2117, 2118
2120→→¬𝜓→↔¬𝜑¬𝜓¬𝜑→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗¬𝜑] into ax-2
2121→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑Modus ponens 2114, 2120
2122→→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑Subs [𝜑↗→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2123→↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑Modus ponens 2121, 2122
2124→→↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑→→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓¬𝜑Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜓↔¬𝜑¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
2125→→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓¬𝜑Modus ponens 2123, 2124
2126→→→¬𝜓¬𝜑→𝜑𝜓→↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓Subs [𝜑↗→→¬𝜓¬𝜑→𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2127→↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓Modus ponens 316, 2126
2128→→↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓→→↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→𝜑𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2
2129→→↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→𝜑𝜓Modus ponens 2127, 2128
2130→↔¬𝜑¬𝜓→𝜑𝜓Modus ponens 2102, 2129
2131→↔¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into biimp
2132→→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2133→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 2131, 2132
2134→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2
2135→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 2133, 2134
2136→→→¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑Subs [𝜑↗→→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2137→↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑Modus ponens ax-3, 2136
2138→→↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑→→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→𝜓𝜑Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→𝜓𝜑] into ax-2
2139→→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→𝜓𝜑Modus ponens 2137, 2138
2140→↔¬𝜑¬𝜓→𝜓𝜑Modus ponens 2131, 2139
2141→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2142→↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Modus ponens 1674, 2141
2143→→↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→↔¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2
2144→→↔¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑Modus ponens 2142, 2143
2145→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑Modus ponens 2140, 2144
2146→→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2147→↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Modus ponens 1681, 2146
2148→→↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2
2149→→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓Modus ponens 2147, 2148
2150→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓Modus ponens 2145, 2149
2151→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2152→→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
2153→→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓Modus ponens 2151, 2152
2154→→→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓→𝜑𝜓] into ax-2
2155→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓Modus ponens 2153, 2154
2156→→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2
2157→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2150, 2156
2158→→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
2159→→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2157, 2158
2160→→→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→↔¬𝜑¬𝜓→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2
2161→→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2159, 2160
2162→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2151, 2161
2163→→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2164→↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2162, 2163
2165→→↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2
2166→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2164, 2165
2167→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2130, 2166
2168→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2169→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2170→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓Modus ponens 2168, 2169
2171→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→↔¬𝜑¬𝜓↔¬𝜑¬𝜓] into ax-2
2172→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓Modus ponens 2170, 2171
2173→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2
2174→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2167, 2173
2175→→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2176→↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2174, 2175
2177→→↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→↔¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2
2178→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2176, 2177
2179→↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 2089, 2174
2180→→↔𝜑𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓↔¬𝜑¬𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into impbi
2181→→↔¬𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2088, 2180
2182↔↔𝜑𝜓↔¬𝜑¬𝜓Modus ponens 2179, 2181notbi
2183→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜒𝜃] into simplim
2184→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜃] into simprim
2185→↔↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into biimp
2186→→↔𝜑𝜓↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2187→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑Modus ponens bicom1, 2186
2188→→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2
2189→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑Modus ponens 2187, 2188
2190→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑Modus ponens 2183, 2189
2191→↔𝜓𝜑→𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗𝜑] into biimp
2192→→↔𝜓𝜑→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑Subs [𝜑↗→↔𝜓𝜑→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2193→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑Modus ponens 2191, 2192
2194→→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2
2195→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Modus ponens 2193, 2194
2196→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Modus ponens 2190, 2195
2197→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2198→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓Subs [𝜑↗→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓] into ax-1
2199→𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓Modus ponens 2197, 2198
2200→→𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→→𝜓𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓Subs [𝜑↗𝜓, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓] into ax-2
2201→→𝜓𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓Modus ponens 2199, 2200
2202→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗𝜑] into ax-2
2203→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑Modus ponens 2196, 2202
2204→→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑] into ax-1
2205→𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑Modus ponens 2203, 2204
2206→→𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑Subs [𝜑↗𝜓, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑] into ax-2
2207→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑Modus ponens 2205, 2206
2208→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑Modus ponens 2197, 2207
2209→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃] into id
2210→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2211→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2212→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃Modus ponens 2210, 2211
2213→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-2
2214→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃Modus ponens 2212, 2213
2215→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗𝜑] into ax-2
2216→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Modus ponens 2208, 2215
2217→→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Subs [𝜑↗→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2218→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Modus ponens 2216, 2217
2219→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→𝜓𝜑] into ax-2
2220→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑Modus ponens 2218, 2219
2221→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗𝜒] into idd
2222→→𝜒𝜒→𝜑→𝜒𝜒Subs [𝜑↗→𝜒𝜒, 𝜓↗𝜑] into ax-1
2223→→→𝜒𝜒→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒Subs [𝜑↗→→𝜒𝜒→𝜑→𝜒𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2224→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒Modus ponens 2222, 2223
2225→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜒𝜒, 𝜒↗→𝜑→𝜒𝜒] into ax-2
2226→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒Modus ponens 2224, 2225
2227→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒Modus ponens 2221, 2226
2228→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒Subs [𝜓↗𝜒] into ax-2
2229→→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒Subs [𝜑↗→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2230→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒Modus ponens 2228, 2229
2231→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑→𝜒𝜒, 𝜒↗→→𝜑𝜒→𝜑𝜒] into ax-2
2232→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒Modus ponens 2230, 2231
2233→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒Modus ponens 2227, 2232
2234→→𝜓𝜑→→𝜑𝜒→𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜒] into ax-1
2235→→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2236→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑Modus ponens 2234, 2235
2237→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜑] into ax-2
2238→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑Modus ponens 2236, 2237
2239→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑Modus ponens 2196, 2238
2240→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜓↗𝜒, 𝜒↗𝜓] into imim2
2241→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗→𝜑𝜒] into ax-1
2242→→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 2240, 2241
2243→→→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜓𝜑→𝜓𝜒] into ax-2
2244→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 2242, 2243
2245→→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2246→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 2244, 2245
2247→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜑𝜒, 𝜒↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒] into ax-2
2248→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 2246, 2247
2249→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 2233, 2248
2250→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜒] into ax-2
2251→→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2252→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Modus ponens 2250, 2251
2253→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒] into ax-2
2254→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Modus ponens 2252, 2253
2255→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Modus ponens 2249, 2254
2256→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜒] into ax-2
2257→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒Modus ponens 2255, 2256
2258→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒Modus ponens 2239, 2257
2259→→↔𝜑𝜓→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→𝜑𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2260→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓Modus ponens biimp, 2259
2261→→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
2262→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓Modus ponens 2260, 2261
2263→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓Modus ponens 2183, 2262
2264→→→𝜒𝜒→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2265→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒Modus ponens 51, 2264
2266→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2
2267→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒Modus ponens 2265, 2266
2268→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒Modus ponens 2221, 2267
2269→→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2270→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Modus ponens 57, 2269
2271→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2
2272→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒Modus ponens 2270, 2271
2273→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒Modus ponens 2268, 2272
2274→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2275→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens 63, 2274
2276→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2
2277→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓Modus ponens 2275, 2276
2278→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓Modus ponens 2263, 2277
2279→→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2280→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 72, 2279
2281→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2
2282→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 2280, 2281
2283→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 2273, 2282
2284→→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2285→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 78, 2284
2286→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2
2287→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 2285, 2286
2288→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 2283, 2287
2289→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2
2290→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒Modus ponens 2288, 2289
2291→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒Modus ponens 2278, 2290
2292→→→𝜑𝜒→𝜓𝜒→→→𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜓𝜒] into impbi
2293→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→𝜓𝜒→𝜑𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2294→→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2295→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Modus ponens 2293, 2294
2296→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒] into ax-2
2297→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Modus ponens 2295, 2296
2298→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Modus ponens 2291, 2297
2299→→→→𝜑𝜒→𝜓𝜒→→→𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2300→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Modus ponens 2292, 2299
2301→→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2302→¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Modus ponens 2300, 2301
2303→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒] into ax-2
2304→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Modus ponens 2302, 2303
2305→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Modus ponens 2298, 2304
2306→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜓𝜒] into id
2307→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2308→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2309→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒Modus ponens 2307, 2308
2310→→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒] into ax-2
2311→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒Modus ponens 2309, 2310
2312→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2313→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2305, 2312
2314→→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2315→→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2313, 2314
2316→→→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2
2317→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2315, 2316
2318→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2307, 2317
2319→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2320→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2318, 2319
2321→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2
2322→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2320, 2321
2323→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2258, 2322
2324→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2325→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2326→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃Modus ponens 2324, 2325
2327→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-2
2328→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃Modus ponens 2326, 2327
2329→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2330→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2323, 2329
2331→→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2332→¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2330, 2331
2333→→¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2
2334→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2332, 2333
2335→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒Modus ponens 2209, 2330
2336→↔𝜒𝜃→𝜓↔𝜒𝜃Subs [𝜑↗↔𝜒𝜃] into ax-1
2337→→↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃Subs [𝜑↗→↔𝜒𝜃→𝜓↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2338→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃Modus ponens 2336, 2337
2339→→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜒𝜃, 𝜒↗→𝜓↔𝜒𝜃] into ax-2
2340→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃Modus ponens 2338, 2339
2341→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃Modus ponens 2184, 2340
2342↔→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into pm5.74
2343→↔→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃Subs [𝜑↗→𝜓↔𝜒𝜃, 𝜓↗↔→𝜓𝜒→𝜓𝜃] into biimp
2344→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃Modus ponens 2342, 2343
2345→→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃Subs [𝜑↗→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2346→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃Modus ponens 2344, 2345
2347→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓↔𝜒𝜃, 𝜒↗↔→𝜓𝜒→𝜓𝜃] into ax-2
2348→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃Modus ponens 2346, 2347
2349→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃Modus ponens 2341, 2348
2350↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜒, 𝜒↗→𝜓𝜒] into pm5.74
2351→↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp
2352→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Modus ponens 2350, 2351
2353↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Modus ponens 2335, 2352
2354↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜃] into pm5.74
2355→↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into biimp
2356→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Modus ponens 2354, 2355
2357↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Modus ponens 2349, 2356
2358→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into biimp
2359→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Modus ponens 2357, 2358
2360→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp
2361→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Modus ponens 2353, 2360
2362→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into ax-1
2363→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Modus ponens 2359, 2362
2364→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into ax-2
2365→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Modus ponens 2363, 2364
2366→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Modus ponens 2361, 2365
2367→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into bicom1
2368↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Modus ponens 2357, 2367
2369→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp
2370→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒Modus ponens 2368, 2369
2371→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into bicom1
2372↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Modus ponens 2353, 2371
2373→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into biimp
2374→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Modus ponens 2372, 2373
2375→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into ax-1
2376→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Modus ponens 2374, 2375
2377→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into ax-2
2378→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Modus ponens 2376, 2377
2379→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒Modus ponens 2370, 2378
2380→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into impbi
2381→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Modus ponens 2366, 2380
2382↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Modus ponens 2379, 2381
2383↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜒, 𝜒↗→𝜓𝜃] into pm5.74
2384→↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into bicom1
2385↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Modus ponens 2383, 2384
2386→↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Subs [𝜑↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃] into biimp
2387→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Modus ponens 2385, 2386
2388→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Modus ponens 2382, 2387
2389→↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜃] into pm3.2im
2390→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔𝜒𝜃] into ax-1
2391→↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Modus ponens 2388, 2390
2392→→↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Subs [𝜑↗↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗↔→𝜑𝜒→𝜓𝜃] into ax-2
2393→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Modus ponens 2391, 2392
2394→→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Subs [𝜑↗→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔𝜑𝜓] into ax-1
2395→↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Modus ponens 2393, 2394
2396→→↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→→↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃] into ax-2
2397→→↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Modus ponens 2395, 2396
2398→↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃Modus ponens 2389, 2397imbi12
2399→→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2400→→↔𝜓𝜑→𝜓𝜑→↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑Subs [𝜑↗→↔𝜓𝜑→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2401→↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑Modus ponens 2191, 2400
2402→→↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑→→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2
2403→→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→𝜓𝜑Modus ponens 2401, 2402
2404→𝜓→↔𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2405→→𝜓→↔𝜑𝜓𝜓→𝜓→𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→𝜓→↔𝜑𝜓𝜓] into ax-1
2406→𝜓→𝜓→↔𝜑𝜓𝜓Modus ponens 2404, 2405
2407→→𝜓→𝜓→↔𝜑𝜓𝜓→→𝜓𝜓→𝜓→↔𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜒↗→↔𝜑𝜓𝜓] into ax-2
2408→→𝜓𝜓→𝜓→↔𝜑𝜓𝜓Modus ponens 2406, 2407
2409→→↔𝜑𝜓→𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜒↗𝜑] into ax-2
2410→→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-1
2411→𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 1940, 2410
2412→→𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→𝜓→↔𝜑𝜓𝜓→𝜓→↔𝜑𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓𝜑] into ax-2
2413→→𝜓→↔𝜑𝜓𝜓→𝜓→↔𝜑𝜓𝜑Modus ponens 2411, 2412
2414→𝜓→↔𝜑𝜓𝜑Modus ponens 2404, 2413
2415→↔𝜑𝜓→𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓] into ax-1
2416→→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2417→↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓Modus ponens 2415, 2416
2418→→↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜓↔𝜑𝜓] into ax-2
2419→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓Modus ponens 2417, 2418
2420→→𝜓→↔𝜑𝜓𝜑→→𝜓↔𝜑𝜓→𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗𝜑] into ax-2
2421→→𝜓↔𝜑𝜓→𝜓𝜑Modus ponens 2414, 2420
2422→→→𝜓↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2423→↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑Modus ponens 2421, 2422
2424→→↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑→→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜓𝜑] into ax-2
2425→→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓𝜑Modus ponens 2423, 2424
2426→↔𝜑𝜓→𝜒𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into idd
2427→→→𝜒𝜒→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒Subs [𝜑↗→→𝜒𝜒→𝜑→𝜒𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2428→↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒Modus ponens 2222, 2427
2429→→↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜑→𝜒𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜑→𝜒𝜒] into ax-2
2430→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜑→𝜒𝜒Modus ponens 2428, 2429
2431→↔𝜑𝜓→𝜑→𝜒𝜒Modus ponens 2426, 2430
2432→→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒Subs [𝜑↗→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2433→↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒Modus ponens 2228, 2432
2434→→↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→→↔𝜑𝜓→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑→𝜒𝜒, 𝜒↗→→𝜑𝜒→𝜑𝜒] into ax-2
2435→→↔𝜑𝜓→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒Modus ponens 2433, 2434
2436→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒Modus ponens 2431, 2435
2437→→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2438→↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑Modus ponens 2234, 2437
2439→→↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜑] into ax-2
2440→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑Modus ponens 2438, 2439
2441→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑Modus ponens biimpr, 2440
2442→→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2443→↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 2244, 2442
2444→→↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜑𝜒, 𝜒↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒] into ax-2
2445→→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 2443, 2444
2446→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒Modus ponens 2436, 2445
2447→→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2448→↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Modus ponens 2250, 2447
2449→→↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒] into ax-2
2450→→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Modus ponens 2448, 2449
2451→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒Modus ponens 2446, 2450
2452→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜒] into ax-2
2453→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒Modus ponens 2451, 2452
2454→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒Modus ponens 2441, 2453
2455→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2456→↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓Modus ponens biimp, 2455
2457→→↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
2458→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓Modus ponens 2456, 2457
2459→→→𝜒𝜒→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2460→↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒Modus ponens 51, 2459
2461→→↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜓→𝜒𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2
2462→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜓→𝜒𝜒Modus ponens 2460, 2461
2463→↔𝜑𝜓→𝜓→𝜒𝜒Modus ponens 2426, 2462
2464→→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2465→↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Modus ponens 57, 2464
2466→→↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→↔𝜑𝜓→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2
2467→→↔𝜑𝜓→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒Modus ponens 2465, 2466
2468→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒Modus ponens 2463, 2467
2469→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2470→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens 63, 2469
2471→→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2
2472→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens 2470, 2471
2473→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens biimp, 2472
2474→→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2475→↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 72, 2474
2476→→↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2
2477→→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 2475, 2476
2478→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 2468, 2477
2479→→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2480→↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 78, 2479
2481→→↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2
2482→→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 2480, 2481
2483→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 2478, 2482
2484→→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2
2485→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 2483, 2484
2486→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 2473, 2485
2487→→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2488→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Modus ponens 2293, 2487
2489→→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒] into ax-2
2490→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Modus ponens 2488, 2489
2491→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒Modus ponens 2486, 2490
2492→→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2493→↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Modus ponens 2300, 2492
2494→→↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒] into ax-2
2495→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Modus ponens 2493, 2494
2496→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒Modus ponens 2491, 2495
2497→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2498→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2499→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒Modus ponens 2497, 2498
2500→→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒] into ax-2
2501→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒Modus ponens 2499, 2500
2502→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2503→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2496, 2502
2504→→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2505→→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2503, 2504
2506→→→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2
2507→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2505, 2506
2508→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2497, 2507
2509→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2510→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2508, 2509
2511→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2
2512→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2510, 2511
2513→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2454, 2512
2514→→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2515→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2513, 2514
2516→→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2517→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2515, 2516
2518→→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2
2519→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 2517, 2518
2520→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒Modus ponens 1651, 2515imbi1
2521→↔𝜑𝜓→𝜒↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into ax-1
2522→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2523→↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓Modus ponens 2521, 2522
2524→→↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜒↔𝜑𝜓] into ax-2
2525→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓Modus ponens 2523, 2524
2526↔→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74
2527→↔→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓Subs [𝜑↗→𝜒↔𝜑𝜓, 𝜓↗↔→𝜒𝜑→𝜒𝜓] into biimp
2528→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓Modus ponens 2526, 2527
2529→→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓Subs [𝜑↗→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2530→↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓Modus ponens 2528, 2529
2531→→↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒↔𝜑𝜓, 𝜒↗↔→𝜒𝜑→𝜒𝜓] into ax-2
2532→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓Modus ponens 2530, 2531
2533→↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓Modus ponens 2521, 2532imbi2
2534→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into id
2535→↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-1
2536→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 1927, 2535
2537↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74
2538→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp
2539→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Modus ponens 2537, 2538
2540↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Modus ponens 2534, 2539
2541↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74
2542→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp
2543→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 2541, 2542
2544↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 2536, 2543
2545→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp
2546→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 2544, 2545
2547→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp
2548→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Modus ponens 2540, 2547
2549→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into ax-1
2550→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 2546, 2549
2551→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into ax-2
2552→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 2550, 2551
2553→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 2548, 2552
2554→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into bicom1
2555↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Modus ponens 2544, 2554
2556→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp
2557→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑Modus ponens 2555, 2556
2558→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into bicom1
2559↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Modus ponens 2540, 2558
2560→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into biimp
2561→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Modus ponens 2559, 2560
2562→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into ax-1
2563→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Modus ponens 2561, 2562
2564→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into ax-2
2565→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Modus ponens 2563, 2564
2566→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒Modus ponens 2557, 2565
2567→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into impbi
2568→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 2553, 2567
2569↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 2566, 2568
2570↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74
2571→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into bicom1
2572↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Modus ponens 2570, 2571
2573→↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp
2574→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Modus ponens 2572, 2573
2575→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Modus ponens 2569, 2574
2576→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into id
2577→↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into ax-1
2578→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 1938, 2577
2579↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74
2580→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp
2581→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Modus ponens 2579, 2580
2582↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Modus ponens 2576, 2581
2583↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74
2584→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into biimp
2585→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 2583, 2584
2586↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 2578, 2585
2587→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into biimp
2588→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 2586, 2587
2589→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp
2590→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Modus ponens 2582, 2589
2591→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into ax-1
2592→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 2588, 2591
2593→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-2
2594→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 2592, 2593
2595→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 2590, 2594
2596→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into bicom1
2597↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Modus ponens 2586, 2596
2598→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp
2599→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓Modus ponens 2597, 2598
2600→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into bicom1
2601↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Modus ponens 2582, 2600
2602→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into biimp
2603→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Modus ponens 2601, 2602
2604→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-1
2605→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Modus ponens 2603, 2604
2606→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into ax-2
2607→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Modus ponens 2605, 2606
2608→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒Modus ponens 2599, 2607
2609→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into impbi
2610→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 2595, 2609
2611↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Modus ponens 2608, 2610
2612↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74
2613→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into bicom1
2614↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2612, 2613
2615→↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp
2616→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2614, 2615
2617→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2611, 2616
2618→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into impbi
2619→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Modus ponens 2575, 2618
2620↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Modus ponens 2617, 2619
2621↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into pm5.74
2622↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into pm5.74
2623→↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into bicom1
2624↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓Modus ponens 2622, 2623
2625→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2626→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓Modus ponens 2624, 2625
2627→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp
2628→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-1
2629→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓Modus ponens 2626, 2628
2630→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
2631→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2629, 2630
2632→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2575, 2631
2633→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1
2634→↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp
2635→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓Modus ponens 2622, 2634
2636→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into bicom1
2637↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2620, 2636
2638→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp
2639→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1
2640→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2617, 2639
2641→→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜒↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-2
2642→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2640, 2641
2643→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2635, 2642
2644→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi
2645→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2632, 2644
2646↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2643, 2645
2647→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2648→↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp
2649→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2621, 2648
2650→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into ax-1
2651→→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2632, 2650
2652→→→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
2653→→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2651, 2652
2654→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2649, 2653
2655→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1
2656↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Modus ponens 2646, 2655
2657→↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp
2658→↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into bicom1
2659↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑Modus ponens 2621, 2658
2660→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp
2661→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑Modus ponens 2659, 2660
2662→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1
2663→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑Modus ponens 2661, 2662
2664→→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜑] into ax-2
2665→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑Modus ponens 2663, 2664
2666→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑Modus ponens 2643, 2665
2667→→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi
2668→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2654, 2667
2669↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2666, 2668
2670↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜑, 𝜒↗↔𝜒𝜓] into pm5.74
2671→↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓] into bicom1
2672↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓Modus ponens 2670, 2671
2673→↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓Subs [𝜑↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓] into biimp
2674→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓Modus ponens 2672, 2673
2675→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓Modus ponens 2669, 2674
2676↔↔𝜑𝜒↔𝜒𝜑Subs [𝜓↗𝜒] into bicom
2677↔↔𝜓𝜒↔𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗𝜒] into bicom
2678→↔↔𝜑𝜒↔𝜒𝜑→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑Subs [𝜑↗↔↔𝜑𝜒↔𝜒𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2679→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑Modus ponens 2676, 2678
2680↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜒𝜑] into pm5.74
2681→↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑] into biimp
2682→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑Modus ponens 2680, 2681
2683↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑Modus ponens 2679, 2682
2684→↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓] into biimp
2685→→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2670, 2684
2686→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2687→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp
2688→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑Modus ponens 2683, 2687
2689→→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into ax-1
2690→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓Modus ponens 2654, 2689
2691→→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
2692→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Modus ponens 2690, 2691
2693→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Modus ponens 2688, 2692
2694→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1
2695↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑Modus ponens 2669, 2694
2696→↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp
2697→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into bicom1
2698↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒Modus ponens 2683, 2697
2699→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into biimp
2700→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒Modus ponens 2698, 2699
2701→→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1
2702→→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒Modus ponens 2700, 2701
2703→→→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
2704→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 2702, 2703
2705→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 2666, 2704
2706→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi
2707→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Modus ponens 2693, 2706
2708↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Modus ponens 2705, 2707
2709↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜒𝜓] into pm5.74
2710→↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓] into bicom1
2711↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓Modus ponens 2709, 2710
2712→↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓Subs [𝜑↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓] into biimp
2713→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓Modus ponens 2711, 2712
2714→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓Modus ponens 2708, 2713
2715→↔↔𝜓𝜒↔𝜒𝜓↔↔𝜒𝜓↔𝜓𝜒Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜒𝜓] into bicom1
2716↔↔𝜒𝜓↔𝜓𝜒Modus ponens 2677, 2715
2717→↔↔𝜒𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒Subs [𝜑↗↔↔𝜒𝜓↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2718→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒Modus ponens 2716, 2717
2719→↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓] into biimp
2720→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Modus ponens 2709, 2719
2721↔→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗↔𝜓𝜒] into pm5.74
2722→↔→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒] into biimp
2723→→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒Modus ponens 2721, 2722
2724↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒Modus ponens 2718, 2723
2725→↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into biimp
2726→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒Modus ponens 2724, 2725
2727→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2728→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into ax-1
2729→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒Modus ponens 2726, 2728
2730→→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2
2731→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 2729, 2730
2732→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 2693, 2731
2733→↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into bicom1
2734↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓Modus ponens 2724, 2733
2735→↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2736→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓Modus ponens 2734, 2735
2737→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1
2738↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 2708, 2737
2739→↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into biimp
2740→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into ax-1
2741→→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 2705, 2740
2742→→→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
2743→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 2741, 2742
2744→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 2736, 2743
2745→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into impbi
2746→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 2732, 2745
2747↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 2744, 2746
2748↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜓𝜒] into pm5.74
2749→↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒] into bicom1
2750↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒Modus ponens 2748, 2749
2751→↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒Subs [𝜑↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒] into biimp
2752→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒Modus ponens 2750, 2751
2753→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒Modus ponens 2747, 2752bibi1
2754→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into biimp
2755→→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒Subs [𝜑↗→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2756→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒Modus ponens 2754, 2755
2757→→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜑𝜒↔𝜓𝜒, 𝜒↗→↔𝜑𝜒↔𝜓𝜒] into ax-2
2758→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒Modus ponens 2756, 2757
2759→↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒Modus ponens bibi1, 2758bitr3
2760↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓Subs [𝜓↗¬𝜓] into notbi
2761→↔¬𝜑𝜓↔¬𝜑𝜓Subs [𝜑↗↔¬𝜑𝜓] into id
2762→↔𝜓¬¬𝜓→↔¬𝜑𝜓↔𝜓¬¬𝜓Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1
2763→↔¬𝜑𝜓↔𝜓¬¬𝜓Modus ponens 1915, 2762
2764↔→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into pm5.74
2765→↔→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓Subs [𝜑↗→↔¬𝜑𝜓↔¬𝜑𝜓, 𝜓↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓] into biimp
2766→→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓Modus ponens 2764, 2765
2767↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓Modus ponens 2761, 2766
2768↔→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74
2769→↔→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓Subs [𝜑↗→↔¬𝜑𝜓↔𝜓¬¬𝜓, 𝜓↗↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓] into biimp
2770→→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓Modus ponens 2768, 2769
2771↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓Modus ponens 2763, 2770
2772→↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into biimp
2773→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓Modus ponens 2771, 2772
2774→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓] into biimp
2775→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓Modus ponens 2767, 2774
2776→→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓Subs [𝜑↗→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓¬𝜑] into ax-1
2777→→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓Modus ponens 2773, 2776
2778→→→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓, 𝜒↗→↔¬𝜑𝜓¬¬𝜓] into ax-2
2779→→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓Modus ponens 2777, 2778
2780→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓Modus ponens 2775, 2779
2781→↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into bicom1
2782↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓Modus ponens 2771, 2781
2783→↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓Subs [𝜑↗→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓𝜓] into biimp
2784→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓Modus ponens 2782, 2783
2785→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓] into bicom1
2786↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑Modus ponens 2767, 2785
2787→↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬𝜑] into biimp
2788→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑Modus ponens 2786, 2787
2789→→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑Subs [𝜑↗→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into ax-1
2790→→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑Modus ponens 2788, 2789
2791→→→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑Subs [𝜑↗→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓𝜓, 𝜒↗→↔¬𝜑𝜓¬𝜑] into ax-2
2792→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑Modus ponens 2790, 2791
2793→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑Modus ponens 2784, 2792
2794→→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into impbi
2795→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓Modus ponens 2780, 2794
2796↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓Modus ponens 2793, 2795
2797↔→↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬¬𝜓] into pm5.74
2798→↔→↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓Subs [𝜑↗→↔¬𝜑𝜓↔¬𝜑¬¬𝜓, 𝜓↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓] into bicom1
2799↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓Modus ponens 2797, 2798
2800→↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓Subs [𝜑↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓↔¬𝜑¬¬𝜓] into biimp
2801→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓Modus ponens 2799, 2800
2802→↔¬𝜑𝜓↔¬𝜑¬¬𝜓Modus ponens 2796, 2801
2803→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓Subs [𝜑↗↔¬𝜑¬¬𝜓] into id
2804→↔𝜓¬¬𝜓↔¬¬𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗¬¬𝜓] into bicom1
2805↔¬¬𝜓𝜓Modus ponens 1915, 2804
2806→↔¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓Subs [𝜑↗↔¬¬𝜓𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into ax-1
2807→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓Modus ponens 2805, 2806
2808↔→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬¬𝜓] into pm5.74
2809→↔→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp
2810→→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓Modus ponens 2808, 2809
2811↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓Modus ponens 2803, 2810
2812↔→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗𝜓] into pm5.74
2813→↔→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓] into biimp
2814→→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓Modus ponens 2812, 2813
2815↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓Modus ponens 2807, 2814
2816→↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into biimp
2817→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓Modus ponens 2815, 2816
2818→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp
2819→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓Modus ponens 2811, 2818
2820→→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓Subs [𝜑↗→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬𝜑] into ax-1
2821→→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓Modus ponens 2817, 2820
2822→→→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜒↗→↔¬𝜑¬¬𝜓𝜓] into ax-2
2823→→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓Modus ponens 2821, 2822
2824→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓Modus ponens 2819, 2823
2825→↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into bicom1
2826↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓Modus ponens 2815, 2825
2827→↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp
2828→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓Modus ponens 2826, 2827
2829→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into bicom1
2830↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑Modus ponens 2811, 2829
2831→↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬𝜑] into biimp
2832→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑Modus ponens 2830, 2831
2833→→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑Subs [𝜑↗→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into ax-1
2834→→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑Modus ponens 2832, 2833
2835→→→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑Subs [𝜑↗→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜒↗→↔¬𝜑¬¬𝜓¬𝜑] into ax-2
2836→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑Modus ponens 2834, 2835
2837→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑Modus ponens 2828, 2836
2838→→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into impbi
2839→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓Modus ponens 2824, 2838
2840↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓Modus ponens 2837, 2839
2841↔→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into pm5.74
2842→↔→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓] into bicom1
2843↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓Modus ponens 2841, 2842
2844→↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓Subs [𝜑↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓] into biimp
2845→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓Modus ponens 2843, 2844
2846→↔¬𝜑¬¬𝜓↔¬𝜑𝜓Modus ponens 2840, 2845
2847→→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into impbi
2848→→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓Modus ponens 2802, 2847
2849↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓Modus ponens 2846, 2848
2850↔↔¬𝜑𝜓↔𝜓¬𝜑Subs [𝜑↗¬𝜑] into bicom
2851→↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into bicom1
2852↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓Modus ponens 2849, 2851
2853→↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into biimp
2854→↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑¬¬𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into biimp
2855→↔𝜑¬𝜓↔¬𝜑¬¬𝜓Modus ponens 2760, 2854
2856→→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into ax-1
2857→↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓Modus ponens 2846, 2856
2858→→↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→→↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓, 𝜒↗↔¬𝜑𝜓] into ax-2
2859→→↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑𝜓Modus ponens 2857, 2858
2860→↔𝜑¬𝜓↔¬𝜑𝜓Modus ponens 2855, 2859
2861→↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into bicom1
2862→↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into biimp
2863→↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into bicom1
2864↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓Modus ponens 2760, 2863
2865→↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔𝜑¬𝜓] into biimp
2866→↔¬𝜑¬¬𝜓↔𝜑¬𝜓Modus ponens 2864, 2865
2867→→↔¬𝜑¬¬𝜓↔𝜑¬𝜓→↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓Subs [𝜑↗→↔¬𝜑¬¬𝜓↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1
2868→↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓Modus ponens 2866, 2867
2869→→↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓→→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2
2870→→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓Modus ponens 2868, 2869
2871→↔¬𝜑𝜓↔𝜑¬𝜓Modus ponens 2802, 2870
2872→→↔𝜑¬𝜓↔¬𝜑𝜓→→↔¬𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓↔¬𝜑𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into impbi
2873→→↔¬𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓↔¬𝜑𝜓Modus ponens 2860, 2872
2874↔↔𝜑¬𝜓↔¬𝜑𝜓Modus ponens 2871, 2873
2875→↔↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜓¬𝜑Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into biimp
2876→↔¬𝜑𝜓↔𝜓¬𝜑Modus ponens 2850, 2875
2877→↔↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔¬𝜑𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into biimp
2878→→↔¬𝜑𝜓↔𝜓¬𝜑→↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑Subs [𝜑↗→↔¬𝜑𝜓↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓] into ax-1
2879→↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑Modus ponens 2876, 2878
2880→→↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑→→↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓, 𝜒↗↔𝜓¬𝜑] into ax-2
2881→→↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑Modus ponens 2879, 2880
2882→↔𝜑¬𝜓↔𝜓¬𝜑Modus ponens 2860, 2881
2883→↔↔¬𝜑𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑↔¬𝜑𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1
2884↔↔𝜓¬𝜑↔¬𝜑𝜓Modus ponens 2850, 2883
2885→↔↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓] into biimp
2886→↔𝜓¬𝜑↔¬𝜑𝜓Modus ponens 2884, 2885
2887→↔↔𝜑¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔𝜑¬𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into bicom1
2888↔↔¬𝜑𝜓↔𝜑¬𝜓Modus ponens 2874, 2887
2889→↔↔¬𝜑𝜓↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into biimp
2890→→↔¬𝜑𝜓↔𝜑¬𝜓→↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓Subs [𝜑↗→↔¬𝜑𝜓↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into ax-1
2891→↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓Modus ponens 2871, 2890
2892→→↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓→→↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔𝜑¬𝜓Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2
2893→→↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔𝜑¬𝜓Modus ponens 2891, 2892
2894→↔𝜓¬𝜑↔𝜑¬𝜓Modus ponens 2886, 2893
2895→→↔𝜑¬𝜓↔𝜓¬𝜑→→↔𝜓¬𝜑↔𝜑¬𝜓↔↔𝜑¬𝜓↔𝜓¬𝜑Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into impbi
2896→→↔𝜓¬𝜑↔𝜑¬𝜓↔↔𝜑¬𝜓↔𝜓¬𝜑Modus ponens 2882, 2895
2897↔↔𝜑¬𝜓↔𝜓¬𝜑Modus ponens 2894, 2896con2bi
2898→→¬𝜓𝜑→¬𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into con1
2899→→→¬𝜑𝜓→¬𝜓𝜑→→→¬𝜓𝜑→¬𝜑𝜓↔→¬𝜑𝜓→¬𝜓𝜑Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜓𝜑] into impbi
2900→→→¬𝜓𝜑→¬𝜑𝜓↔→¬𝜑𝜓→¬𝜓𝜑Modus ponens con1, 2899
2901↔→¬𝜑𝜓→¬𝜓𝜑Modus ponens 2898, 2900con1b
2902→→𝜓¬𝜑→𝜑¬𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into con2
2903→→→𝜑¬𝜓→𝜓¬𝜑→→→𝜓¬𝜑→𝜑¬𝜓↔→𝜑¬𝜓→𝜓¬𝜑Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜓¬𝜑] into impbi
2904→→→𝜓¬𝜑→𝜑¬𝜓↔→𝜑¬𝜓→𝜓¬𝜑Modus ponens con2, 2903
2905↔→𝜑¬𝜓→𝜓¬𝜑Modus ponens 2902, 2904con2b
2906→→𝜓→𝜑𝜓→𝜑→𝜓→𝜑𝜓Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1
2907→𝜑→𝜓→𝜑𝜓Modus ponens 208, 2906
2908→→→𝜑𝜓𝜓→→𝜓→𝜑𝜓↔→𝜑𝜓𝜓Subs [𝜑↗→𝜑𝜓] into impbi
2909→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1
2910→→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓Subs [𝜑↗→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1
2911→𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓Modus ponens 2909, 2910
2912→→𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→𝜑→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓Subs [𝜓↗→𝜓→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜓→𝜓→𝜑𝜓] into ax-2
2913→→𝜑→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓Modus ponens 2911, 2912
2914→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓Modus ponens 2907, 2913
2915→→→→𝜑𝜓𝜓→→𝜓→𝜑𝜓↔→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→𝜓→𝜑𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2
2916→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓Modus ponens 2908, 2915
2917→→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓Subs [𝜑↗→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2918→𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓Modus ponens 2916, 2917
2919→→𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓Subs [𝜓↗→→→𝜑𝜓𝜓→𝜓→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓] into ax-2
2920→→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓Modus ponens 2918, 2919
2921→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓Modus ponens 2914, 2920
2922→→→𝜑𝜓𝜓→→𝜑𝜓𝜓Subs [𝜑↗→→𝜑𝜓𝜓] into id
2923→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2924→→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓Subs [𝜑↗→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1
2925→→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓Modus ponens 2923, 2924
2926→→→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓, 𝜒↗→𝜑→→𝜑𝜓𝜓] into ax-2
2927→→→→𝜑𝜓𝜓→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓Modus ponens 2925, 2926
2928→→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2
2929→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Modus ponens 2921, 2928
2930→→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Subs [𝜑↗→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1
2931→→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Modus ponens 2929, 2930
2932→→→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→𝜑→→𝜑𝜓𝜓, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2
2933→→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Modus ponens 2931, 2932
2934→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Modus ponens 2923, 2933
2935→→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Subs [𝜑↗→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2936→𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓Modus ponens 2934, 2935
2937→→𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑→𝜑↔→𝜑𝜓𝜓Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2
2938→→𝜑→→𝜑𝜓𝜓→𝜑→𝜑↔→𝜑𝜓𝜓Modus ponens 2936, 2937
2939→𝜑→𝜑↔→𝜑𝜓𝜓Modus ponens pm2.27, 2938
2940→→𝜑→𝜑𝜑→𝜑→𝜑→𝜑𝜑Subs [𝜑↗→𝜑→𝜑𝜑, 𝜓↗𝜑] into ax-1
2941→𝜑→𝜑→𝜑𝜑Modus ponens 5, 2940
2942→→𝜑→𝜑→𝜑𝜑→→𝜑𝜑→𝜑→𝜑𝜑Subs [𝜓↗𝜑, 𝜒↗→𝜑𝜑] into ax-2
2943→→𝜑𝜑→𝜑→𝜑𝜑Modus ponens 2941, 2942
2944→→𝜑→𝜑↔→𝜑𝜓𝜓→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓Subs [𝜓↗𝜑, 𝜒↗↔→𝜑𝜓𝜓] into ax-2
2945→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓Modus ponens 2939, 2944
2946→→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓→𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓Subs [𝜑↗→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2947→𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓Modus ponens 2945, 2946
2948→→𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜑𝜓𝜓Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2
2949→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜑𝜓𝜓Modus ponens 2947, 2948
2950→𝜑↔→𝜑𝜓𝜓Modus ponens id, 2945pm5.5
2951↔↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓] into bicom
2952→↔↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓Subs [𝜑↗↔→𝜑𝜓𝜓, 𝜓↗↔𝜓→𝜑𝜓] into biimp
2953→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓Modus ponens 2951, 2952
2954→→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1
2955→𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓Modus ponens 2953, 2954
2956→→𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→→𝜑↔→𝜑𝜓𝜓→𝜑↔𝜓→𝜑𝜓Subs [𝜓↗↔→𝜑𝜓𝜓, 𝜒↗↔𝜓→𝜑𝜓] into ax-2
2957→→𝜑↔→𝜑𝜓𝜓→𝜑↔𝜓→𝜑𝜓Modus ponens 2955, 2956
2958→𝜑↔𝜓→𝜑𝜓Modus ponens pm5.5, 2957biimt
2959↔↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓] into bicom
2960→↔↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓Subs [𝜑↗↔𝜓→𝜑𝜓, 𝜓↗↔→𝜑𝜓𝜓] into biimp
2961→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓Modus ponens 2959, 2960
2962→→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓Subs [𝜑↗→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2963→𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓Modus ponens 2961, 2962
2964→→𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→→𝜑↔𝜓→𝜑𝜓→𝜑↔→𝜑𝜓𝜓Subs [𝜓↗↔𝜓→𝜑𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2
2965→→𝜑↔𝜓→𝜑𝜓→𝜑↔→𝜑𝜓𝜓Modus ponens 2963, 2964
2966→¬𝜑↔¬𝜓→¬𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into biimt
2967↔→𝜓𝜑→¬𝜑¬𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into con34b
2968→↔→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗→¬𝜑¬𝜓] into bicom1
2969↔→¬𝜑¬𝜓→𝜓𝜑Modus ponens 2967, 2968
2970→↔→¬𝜑¬𝜓→𝜓𝜑→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑Subs [𝜑↗↔→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗¬𝜑] into ax-1
2971→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑Modus ponens 2969, 2970
2972↔→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗→¬𝜑¬𝜓] into pm5.74
2973→↔→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔¬𝜓→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓] into biimp
2974→→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓Modus ponens 2972, 2973
2975↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓Modus ponens 2966, 2974
2976↔→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→𝜓𝜑] into pm5.74
2977→↔→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Subs [𝜑↗→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑] into biimp
2978→→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Modus ponens 2976, 2977
2979↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Modus ponens 2971, 2978
2980→↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into biimp
2981→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Modus ponens 2979, 2980
2982→↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into biimp
2983→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓Modus ponens 2975, 2982
2984→→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Subs [𝜑↗→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑¬𝜓] into ax-1
2985→→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Modus ponens 2981, 2984
2986→→→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓, 𝜒↗→¬𝜑→𝜓𝜑] into ax-2
2987→→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Modus ponens 2985, 2986
2988→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Modus ponens 2983, 2987
2989→↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into bicom1
2990↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓Modus ponens 2979, 2989
2991→↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into biimp
2992→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓Modus ponens 2990, 2991
2993→↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into bicom1
2994↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 2975, 2993
2995→↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp
2996→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 2994, 2995
2997→→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into ax-1
2998→→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 2996, 2997
2999→→→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑→¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2
3000→→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓Modus ponens 2998, 2999
3001→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓Modus ponens 2992, 3000
3002→→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into impbi
3003→→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Modus ponens 2988, 3002
3004↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Modus ponens 3001, 3003
3005↔→¬𝜑↔¬𝜓→𝜓𝜑↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗→𝜓𝜑] into pm5.74
3006→↔→¬𝜑↔¬𝜓→𝜓𝜑↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑Subs [𝜑↗→¬𝜑↔¬𝜓→𝜓𝜑, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑] into bicom1
3007↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑Modus ponens 3005, 3006
3008→↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑→↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑↔¬𝜓→𝜓𝜑] into biimp
3009→↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑Modus ponens 3007, 3008
3010→¬𝜑↔¬𝜓→𝜓𝜑Modus ponens 3004, 3009mtt
3011→¬𝜓↔¬𝜑→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into mtt
3012↔↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓] into bicom
3013→↔↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑Subs [𝜑↗↔¬𝜑→𝜑𝜓, 𝜓↗↔→𝜑𝜓¬𝜑] into biimp
3014→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑Modus ponens 3012, 3013
3015→→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑Subs [𝜑↗→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
3016→¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑Modus ponens 3014, 3015
3017→→¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→→¬𝜓↔¬𝜑→𝜑𝜓→¬𝜓↔→𝜑𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑→𝜑𝜓, 𝜒↗↔→𝜑𝜓¬𝜑] into ax-2
3018→→¬𝜓↔¬𝜑→𝜑𝜓→¬𝜓↔→𝜑𝜓¬𝜑Modus ponens 3016, 3017
3019→¬𝜓↔→𝜑𝜓¬𝜑Modus ponens 3011, 3018imnot
3020→𝜑→↔𝜑𝜓𝜑Subs [𝜓↗↔𝜑𝜓] into ax-1
3021→→𝜑→↔𝜑𝜓𝜑→𝜑→𝜑→↔𝜑𝜓𝜑Subs [𝜑↗→𝜑→↔𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1
3022→𝜑→𝜑→↔𝜑𝜓𝜑Modus ponens 3020, 3021
3023→→𝜑→𝜑→↔𝜑𝜓𝜑→→𝜑𝜑→𝜑→↔𝜑𝜓𝜑Subs [𝜓↗𝜑, 𝜒↗→↔𝜑𝜓𝜑] into ax-2
3024→→𝜑𝜑→𝜑→↔𝜑𝜓𝜑Modus ponens 3022, 3023
3025→→↔𝜑𝜓→𝜑𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
3026→→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
3027→𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓Modus ponens 1929, 3026
3028→→𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→𝜑→↔𝜑𝜓𝜑→𝜑→↔𝜑𝜓𝜓Subs [𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into ax-2
3029→→𝜑→↔𝜑𝜓𝜑→𝜑→↔𝜑𝜓𝜓Modus ponens 3027, 3028
3030→𝜑→↔𝜑𝜓𝜓Modus ponens 3020, 3029
3031→→𝜓↔𝜑𝜓→→↔𝜑𝜓𝜓↔𝜓↔𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into impbi
3032→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1
3033→→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓Subs [𝜑↗→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
3034→𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓Modus ponens 3032, 3033
3035→→𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜑→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓Subs [𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓] into ax-2
3036→→𝜑→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓Modus ponens 3034, 3035
3037→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓Modus ponens 3030, 3036
3038→→→𝜓↔𝜑𝜓→→↔𝜑𝜓𝜓↔𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2
3039→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓Modus ponens 3031, 3038
3040→→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓Subs [𝜑↗→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
3041→𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓Modus ponens 3039, 3040
3042→→𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓Subs [𝜓↗→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓, 𝜒↗→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓] into ax-2
3043→→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓Modus ponens 3041, 3042
3044→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓Modus ponens 3037, 3043
3045→→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓Subs [𝜑↗→𝜓↔𝜑𝜓] into id
3046→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
3047→→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1
3048→→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓Modus ponens 3046, 3047
3049→→→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜑→𝜓↔𝜑𝜓] into ax-2
3050→→→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓Modus ponens 3048, 3049
3051→→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Subs [𝜓↗→𝜓↔𝜑𝜓, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2
3052→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Modus ponens 3044, 3051
3053→→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Subs [𝜑↗→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1
3054→→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Modus ponens 3052, 3053
3055→→→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→𝜑→𝜓↔𝜑𝜓, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2
3056→→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Modus ponens 3054, 3055
3057→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Modus ponens 3046, 3056
3058→→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
3059→𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓Modus ponens 3057, 3058
3060→→𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑→𝜑↔𝜓↔𝜑𝜓Subs [𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2
3061→→𝜑→𝜓↔𝜑𝜓→𝜑→𝜑↔𝜓↔𝜑𝜓Modus ponens 3059, 3060
3062→𝜑→𝜑↔𝜓↔𝜑𝜓Modus ponens pm5.1im, 3061
3063→→𝜑→𝜑↔𝜓↔𝜑𝜓→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓Subs [𝜓↗𝜑, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2
3064→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓Modus ponens 3062, 3063
3065→→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓→𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓Subs [𝜑↗→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
3066→𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓Modus ponens 3064, 3065
3067→→𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓↔𝜑𝜓Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2
3068→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓↔𝜑𝜓Modus ponens 3066, 3067
3069→𝜑↔𝜓↔𝜑𝜓Modus ponens id, 3064pm5.501
3070↔→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜒↗↔𝜑𝜓] into pm5.74
3071→↔→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜓↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3072→→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3070, 3071
3073↔→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens pm5.501, 3072ibib
3074→↔↔𝜑𝜓↔𝜓𝜑→𝜑↔↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗𝜑] into ax-1
3075→𝜑↔↔𝜑𝜓↔𝜓𝜑Modus ponens bicom, 3074
3076↔→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑Subs [𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into pm5.74
3077→↔→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑Subs [𝜑↗→𝜑↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑] into biimp
3078→→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 3076, 3077
3079↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 3075, 3078
3080→↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into biimp
3081→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 3079, 3080
3082→↔→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓] into biimp
3083→→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑Subs [𝜑↗→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1
3084→→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 3081, 3083
3085→→→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑↔𝜓𝜑] into ax-2
3086→→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 3084, 3085
3087→→𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 1697, 3086
3088→↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into bicom1
3089↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓Modus ponens 3079, 3088
3090→↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜑𝜓] into biimp
3091→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓Modus ponens 3089, 3090
3092→↔→𝜑𝜓→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓] into bicom1
3093↔→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens ibib, 3092
3094→↔→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp
3095→→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3093, 3094
3096→→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into ax-1
3097→→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3095, 3096
3098→→→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓→→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑𝜓Subs [𝜑↗→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
3099→→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑𝜓Modus ponens 3097, 3098
3100→→𝜑↔𝜓𝜑→𝜑𝜓Modus ponens 3091, 3099
3101→→→𝜑𝜓→𝜑↔𝜓𝜑→→→𝜑↔𝜓𝜑→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into impbi
3102→→→𝜑↔𝜓𝜑→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 3087, 3101
3103↔→𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 3100, 3102ibibr
3104↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑Subs [𝜒↗↔𝜓𝜑] into pm5.74
3105→↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑Subs [𝜑↗→𝜑↔𝜓↔𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑↔𝜓𝜑] into bicom1
3106↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑Modus ponens 3104, 3105
3107→↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑→↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜓↔𝜓𝜑] into biimp
3108→↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑Modus ponens 3106, 3107
3109→𝜑↔𝜓↔𝜓𝜑Modus ponens ibibr, 3108
3110→↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑Subs [𝜑↗→𝜑↔𝜓↔𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑↔𝜓𝜑] into biimp
3111→→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑Modus ponens 3104, 3110
3112→¬𝜑↔¬𝜓↔¬𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into pm5.501
3113→↔↔𝜑𝜓↔¬𝜑¬𝜓↔↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into bicom1
3114↔↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens notbi, 3113
3115→↔↔¬𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
3116→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓Modus ponens 3114, 3115
3117↔→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔¬𝜑¬𝜓] into pm5.74
3118→↔→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓] into biimp
3119→→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓Modus ponens 3117, 3118
3120↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓Modus ponens 3112, 3119
3121↔→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74
3122→↔→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp
3123→→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3121, 3122
3124↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3116, 3123
3125→↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into biimp
3126→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3124, 3125
3127→↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into biimp
3128→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓Modus ponens 3120, 3127
3129→→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1
3130→→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3126, 3129
3131→→→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2
3132→→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3130, 3131
3133→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3128, 3132
3134→↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into bicom1
3135↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓Modus ponens 3124, 3134
3136→↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into biimp
3137→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓Modus ponens 3135, 3136
3138→↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into bicom1
3139↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3120, 3138
3140→↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp
3141→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3139, 3140
3142→→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into ax-1
3143→→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3141, 3142
3144→→→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2
3145→→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3143, 3144
3146→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3137, 3145
3147→→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into impbi
3148→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3133, 3147
3149↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3146, 3148
3150↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74
3151→↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓Subs [𝜑↗→¬𝜑↔¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1
3152↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓Modus ponens 3150, 3151
3153→↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓↔𝜑𝜓] into biimp
3154→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓Modus ponens 3152, 3153
3155→¬𝜑↔¬𝜓↔𝜑𝜓Modus ponens 3149, 3154nbn2
3156→¬𝜓↔¬𝜑↔𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗𝜑] into nbn2
3157↔↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into bicom
3158→↔↔𝜓𝜑↔𝜑𝜓→¬𝜓↔↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗¬𝜓] into ax-1
3159→¬𝜓↔↔𝜓𝜑↔𝜑𝜓Modus ponens 3157, 3158
3160↔→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜓𝜑] into pm5.74
3161→↔→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑Subs [𝜑↗→¬𝜓↔¬𝜑↔𝜓𝜑, 𝜓↗↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑] into biimp
3162→→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑Modus ponens 3160, 3161
3163↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑Modus ponens 3156, 3162
3164↔→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓Subs [𝜑↗¬𝜓, 𝜓↗↔𝜓𝜑, 𝜒↗↔𝜑𝜓] into pm5.74
3165→↔→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓Subs [𝜑↗→¬𝜓↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓] into biimp
3166→→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓Modus ponens 3164, 3165
3167↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓Modus ponens 3159, 3166
3168→↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into biimp
3169→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓Modus ponens 3167, 3168
3170→↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑] into biimp
3171→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑Modus ponens 3163, 3170
3172→→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓Subs [𝜑↗→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓¬𝜑] into ax-1
3173→→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓Modus ponens 3169, 3172
3174→→→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑, 𝜒↗→¬𝜓↔𝜑𝜓] into ax-2
3175→→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓Modus ponens 3173, 3174
3176→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓Modus ponens 3171, 3175
3177→↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into bicom1
3178↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑Modus ponens 3167, 3177
3179→↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑Subs [𝜑↗→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔𝜓𝜑] into biimp
3180→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑Modus ponens 3178, 3179
3181→↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑] into bicom1
3182↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑Modus ponens 3163, 3181
3183→↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓¬𝜑] into biimp
3184→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑Modus ponens 3182, 3183
3185→→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑Subs [𝜑↗→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into ax-1
3186→→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑Modus ponens 3184, 3185
3187→→→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑Subs [𝜑↗→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔𝜓𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2
3188→→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑Modus ponens 3186, 3187
3189→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑Modus ponens 3180, 3188
3190→→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into impbi
3191→→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓Modus ponens 3176, 3190
3192↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓Modus ponens 3189, 3191
3193↔→¬𝜓↔¬𝜑↔𝜑𝜓↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜑𝜓] into pm5.74
3194→↔→¬𝜓↔¬𝜑↔𝜑𝜓↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜓↔¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓] into bicom1
3195↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓Modus ponens 3193, 3194
3196→↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓→↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔¬𝜑↔𝜑𝜓] into biimp
3197→↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓Modus ponens 3195, 3196
3198→¬𝜓↔¬𝜑↔𝜑𝜓Modus ponens 3192, 3197
3199↔↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗↔𝜑𝜓] into bicom
3200→↔↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑Subs [𝜑↗↔¬𝜑↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬𝜑] into biimp
3201→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑Modus ponens 3199, 3200
3202→→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑Subs [𝜑↗→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
3203→¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑Modus ponens 3201, 3202
3204→→¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→→¬𝜓↔¬𝜑↔𝜑𝜓→¬𝜓↔↔𝜑𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬𝜑] into ax-2
3205→→¬𝜓↔¬𝜑↔𝜑𝜓→¬𝜓↔↔𝜑𝜓¬𝜑Modus ponens 3203, 3204
3206→¬𝜓↔↔𝜑𝜓¬𝜑Modus ponens 3198, 3205bibif
3207→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑𝜓] into biimp
3208→→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓→¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓Subs [𝜑↗→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
3209→¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓Modus ponens 3207, 3208
3210→→¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓→→¬𝜑↔¬𝜓↔𝜑𝜓→¬𝜑→¬𝜓↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓↔𝜑𝜓, 𝜒↗→¬𝜓↔𝜑𝜓] into ax-2
3211→→¬𝜑↔¬𝜓↔𝜑𝜓→¬𝜑→¬𝜓↔𝜑𝜓Modus ponens 3209, 3210
3212→¬𝜑→¬𝜓↔𝜑𝜓Modus ponens nbn2, 3211pm5.21im
3213→𝜑↔¬𝜓↔𝜑¬𝜓Subs [𝜓↗¬𝜓] into pm5.501
3214↔↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑¬𝜓] into bicom
3215→↔↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓Subs [𝜑↗↔¬𝜓↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬𝜓] into biimp
3216→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓Modus ponens 3214, 3215
3217→→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓Subs [𝜑↗→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1
3218→𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓Modus ponens 3216, 3217
3219→→𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→→𝜑↔¬𝜓↔𝜑¬𝜓→𝜑↔↔𝜑¬𝜓¬𝜓Subs [𝜓↗↔¬𝜓↔𝜑¬𝜓, 𝜒↗↔↔𝜑¬𝜓¬𝜓] into ax-2
3220→→𝜑↔¬𝜓↔𝜑¬𝜓→𝜑↔↔𝜑¬𝜓¬𝜓Modus ponens 3218, 3219
3221→𝜑↔↔𝜑¬𝜓¬𝜓Modus ponens 3213, 3220
3222↔↔𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓Subs [𝜑↗𝜓, 𝜓↗↔𝜑¬𝜓] into con2bi
3223→↔↔𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓Subs [𝜑↗↔𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬𝜓] into bicom1
3224↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓Modus ponens 3222, 3223
3225→↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓Subs [𝜑↗↔↔𝜑¬𝜓¬𝜓, 𝜓↗↔𝜓¬↔𝜑¬𝜓] into biimp
3226→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓Modus ponens 3224, 3225
3227→→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓Subs [𝜑↗→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑] into ax-1
3228→𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓Modus ponens 3226, 3227
3229→→𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→→𝜑↔↔𝜑¬𝜓¬𝜓→𝜑↔𝜓¬↔𝜑¬𝜓Subs [𝜓↗↔↔𝜑¬𝜓¬𝜓, 𝜒↗↔𝜓¬↔𝜑¬𝜓] into ax-2
3230→→𝜑↔↔𝜑¬𝜓¬𝜓→𝜑↔𝜓¬↔𝜑¬𝜓Modus ponens 3228, 3229
3231→𝜑↔𝜓¬↔𝜑¬𝜓Modus ponens 3221, 3230
3232↔↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom
3233→↔↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓Subs [𝜑↗↔𝜓¬↔𝜑¬𝜓, 𝜓↗↔¬↔𝜑¬𝜓𝜓] into biimp
3234→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓Modus ponens 3232, 3233
3235→→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓Subs [𝜑↗→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓, 𝜓↗𝜑] into ax-1
3236→𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓Modus ponens 3234, 3235
3237→→𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→→𝜑↔𝜓¬↔𝜑¬𝜓→𝜑↔¬↔𝜑¬𝜓𝜓Subs [𝜓↗↔𝜓¬↔𝜑¬𝜓, 𝜒↗↔¬↔𝜑¬𝜓𝜓] into ax-2
3238→→𝜑↔𝜓¬↔𝜑¬𝜓→𝜑↔¬↔𝜑¬𝜓𝜓Modus ponens 3236, 3237
3239→𝜑↔¬↔𝜑¬𝜓𝜓Modus ponens 3231, 3238
3240↔→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓Subs [𝜓↗¬↔𝜑¬𝜓, 𝜒↗𝜓] into pm5.74
3241→↔→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑↔¬↔𝜑¬𝜓𝜓, 𝜓↗↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓] into biimp
3242→→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓Modus ponens 3240, 3241
3243↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓Modus ponens 3239, 3242
3244→↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓] into biimp
3245→→𝜑¬↔𝜑¬𝜓→𝜑𝜓Modus ponens 3243, 3244
3246→→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑¬↔𝜑¬𝜓] into ax-1
3247→→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 1697, 3246
3248→→→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2
3249→→→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓Modus ponens 3247, 3248
3250→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓Modus ponens 3245, 3249
3251→↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓] into bicom1
3252↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓Modus ponens 3243, 3251
3253→↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬↔𝜑¬𝜓] into biimp
3254→→𝜑𝜓→𝜑¬↔𝜑¬𝜓Modus ponens 3252, 3253
3255→→→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓Subs [𝜑↗→→𝜑𝜓→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑↔𝜑𝜓] into ax-1
3256→→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓Modus ponens 3254, 3255
3257→→→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬↔𝜑¬𝜓] into ax-2
3258→→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓Modus ponens 3256, 3257
3259→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓Modus ponens 3095, 3258
3260→→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑↔𝜑𝜓] into impbi
3261→→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓Modus ponens 3250, 3260
3262↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓Modus ponens 3259, 3261
3263↔→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓Subs [𝜓↗¬↔𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74
3264→↔→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓] into bicom1
3265↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Modus ponens 3263, 3264
3266→↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓] into biimp
3267→↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Modus ponens 3265, 3266
3268→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Modus ponens 3262, 3267
3269↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬↔𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into bicom
3270→↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into biimp
3271→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3269, 3270
3272→→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑] into ax-1
3273→𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3271, 3272
3274→→𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜓↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3275→→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3273, 3274
3276→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3268, 3275
3277→¬𝜑↔¬¬𝜓↔𝜑¬𝜓Subs [𝜓↗¬𝜓] into nbn2
3278↔↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑¬𝜓] into bicom
3279→↔↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓Subs [𝜑↗↔¬¬𝜓↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓] into biimp
3280→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓Modus ponens 3278, 3279
3281→→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓Subs [𝜑↗→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1
3282→¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓Modus ponens 3280, 3281
3283→→¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→→¬𝜑↔¬¬𝜓↔𝜑¬𝜓→¬𝜑↔↔𝜑¬𝜓¬¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔¬¬𝜓↔𝜑¬𝜓, 𝜒↗↔↔𝜑¬𝜓¬¬𝜓] into ax-2
3284→→¬𝜑↔¬¬𝜓↔𝜑¬𝜓→¬𝜑↔↔𝜑¬𝜓¬¬𝜓Modus ponens 3282, 3283
3285→¬𝜑↔↔𝜑¬𝜓¬¬𝜓Modus ponens 3277, 3284
3286↔↔¬𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑¬𝜓] into con2bi
3287→↔↔¬𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓Subs [𝜑↗↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓] into bicom1
3288↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓Modus ponens 3286, 3287
3289→↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓Subs [𝜑↗↔↔𝜑¬𝜓¬¬𝜓, 𝜓↗↔¬𝜓¬↔𝜑¬𝜓] into biimp
3290→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓Modus ponens 3288, 3289
3291→→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓Subs [𝜑↗→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3292→¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓Modus ponens 3290, 3291
3293→→¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→→¬𝜑↔↔𝜑¬𝜓¬¬𝜓→¬𝜑↔¬𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓, 𝜒↗↔¬𝜓¬↔𝜑¬𝜓] into ax-2
3294→→¬𝜑↔↔𝜑¬𝜓¬¬𝜓→¬𝜑↔¬𝜓¬↔𝜑¬𝜓Modus ponens 3292, 3293
3295→¬𝜑↔¬𝜓¬↔𝜑¬𝜓Modus ponens 3285, 3294
3296↔↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom
3297→↔↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓Subs [𝜑↗↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗↔¬↔𝜑¬𝜓¬𝜓] into biimp
3298→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓Modus ponens 3296, 3297
3299→→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓Subs [𝜑↗→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓, 𝜓↗¬𝜑] into ax-1
3300→¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓Modus ponens 3298, 3299
3301→→¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→→¬𝜑↔¬𝜓¬↔𝜑¬𝜓→¬𝜑↔¬↔𝜑¬𝜓¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓¬↔𝜑¬𝜓, 𝜒↗↔¬↔𝜑¬𝜓¬𝜓] into ax-2
3302→→¬𝜑↔¬𝜓¬↔𝜑¬𝜓→¬𝜑↔¬↔𝜑¬𝜓¬𝜓Modus ponens 3300, 3301
3303→¬𝜑↔¬↔𝜑¬𝜓¬𝜓Modus ponens 3295, 3302
3304↔→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑¬𝜓, 𝜒↗¬𝜓] into pm5.74
3305→↔→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔¬↔𝜑¬𝜓¬𝜓, 𝜓↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓] into biimp
3306→→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3304, 3305
3307↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3303, 3306
3308→↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑↔¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp
3309→→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3150, 3308
3310→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into biimp
3311→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp
3312→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3307, 3311
3313→→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬↔𝜑¬𝜓] into ax-1
3314→→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3133, 3313
3315→→→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2
3316→→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3314, 3315
3317→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3312, 3316
3318→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into bicom1
3319↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3149, 3318
3320→↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp
3321→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into bicom1
3322↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓Modus ponens 3307, 3321
3323→↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬↔𝜑¬𝜓] into biimp
3324→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓Modus ponens 3322, 3323
3325→→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into ax-1
3326→→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓Modus ponens 3324, 3325
3327→→→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑¬↔𝜑¬𝜓] into ax-2
3328→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓Modus ponens 3326, 3327
3329→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓Modus ponens 3146, 3328
3330→→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into impbi
3331→→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3317, 3330
3332↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3329, 3331
3333↔→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74
3334→↔→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1
3335↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Modus ponens 3333, 3334
3336→↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓] into biimp
3337→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Modus ponens 3335, 3336
3338→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓Modus ponens 3332, 3337
3339→→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3340→¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3271, 3339
3341→→¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3342→→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3340, 3341
3343→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3338, 3342
3344→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into id
3345→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3346→¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3344, 3345
3347→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into notnotr
3348→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3349→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1
3350→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3348, 3349
3351→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3352→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3350, 3351
3353→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3347, 3352
3354→→¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3355→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3346, 3354
3356→→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1
3357→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3355, 3356
3358→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3359→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3357, 3358
3360→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1
3361→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
3362→¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑Modus ponens 3360, 3361
3363→→¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑] into ax-2
3364→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑Modus ponens 3362, 3363
3365→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3366→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3353, 3365
3367→→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3368→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3366, 3367
3369→→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑, 𝜒↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3370→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3368, 3369
3371→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3360, 3370
3372→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-3
3373→→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3374→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3372, 3373
3375→→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3376→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3374, 3375
3377→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3371, 3376
3378→→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3379→→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3377, 3378
3380→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3343, 3379
3381→→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑Subs [𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-3
3382→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑Modus ponens 3380, 3381
3383→→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1
3384→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3276, 3383
3385→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3386→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3384, 3385
3387→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3382, 3386
3388→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓Subs [𝜑↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into pm2.18
3389↔↔𝜑𝜓¬↔𝜑¬𝜓Modus ponens 3387, 3388pm5.18
3390↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓Subs [𝜑↗↔𝜑¬𝜓] into notnotb
3391→↔↔𝜑𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom1
3392↔¬↔𝜑¬𝜓↔𝜑𝜓Modus ponens pm5.18, 3391
3393↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into notbi
3394→↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓→↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓] into biimp
3395→↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3393, 3394
3396↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3392, 3395
3397→↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into biimp
3398→¬¬↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3396, 3397
3399→↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬¬↔𝜑¬𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into biimp
3400→↔𝜑¬𝜓¬¬↔𝜑¬𝜓Modus ponens 3390, 3399
3401→→¬¬↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗→¬¬↔𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into ax-1
3402→↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3398, 3401
3403→→↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓→→↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓, 𝜒↗¬↔𝜑𝜓] into ax-2
3404→→↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3402, 3403
3405→↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3400, 3404
3406→↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into bicom1
3407↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓Modus ponens 3396, 3406
3408→↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓¬¬↔𝜑¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into biimp
3409→¬↔𝜑𝜓¬¬↔𝜑¬𝜓Modus ponens 3407, 3408
3410→↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into bicom1
3411↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓Modus ponens 3390, 3410
3412→↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗↔𝜑¬𝜓] into biimp
3413→¬¬↔𝜑¬𝜓↔𝜑¬𝜓Modus ponens 3411, 3412
3414→→¬¬↔𝜑¬𝜓↔𝜑¬𝜓→¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓Subs [𝜑↗→¬¬↔𝜑¬𝜓↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
3415→¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓Modus ponens 3413, 3414
3416→→¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓→→¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬↔𝜑¬𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2
3417→→¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓Modus ponens 3415, 3416
3418→¬↔𝜑𝜓↔𝜑¬𝜓Modus ponens 3409, 3417
3419→→↔𝜑¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into impbi
3420→→¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3405, 3419
3421↔↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3418, 3420
3422→↔↔𝜑¬𝜓¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜑¬𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into bicom1
3423↔¬↔𝜑𝜓↔𝜑¬𝜓Modus ponens 3421, 3422xor3
3424→↔↔𝜑¬𝜓↔𝜓¬𝜑→↔𝜑¬𝜓↔𝜓¬𝜑Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into biimp
3425→↔¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into biimp
3426→→↔𝜑¬𝜓↔𝜓¬𝜑→¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑Subs [𝜑↗→↔𝜑¬𝜓↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1
3427→¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑Modus ponens 2882, 3426
3428→→¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑→→¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜓¬𝜑Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓, 𝜒↗↔𝜓¬𝜑] into ax-2
3429→→¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜓¬𝜑Modus ponens 3427, 3428
3430→¬↔𝜑𝜓↔𝜓¬𝜑Modus ponens 3418, 3429
3431→↔↔𝜑¬𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑↔𝜑¬𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1
3432↔↔𝜓¬𝜑↔𝜑¬𝜓Modus ponens con2bi, 3431
3433→↔↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑↔𝜑¬𝜓Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓] into biimp
3434→↔¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into bicom1
3435→↔↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into biimp
3436→→↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗→↔𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into ax-1
3437→↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓Modus ponens 3405, 3436
3438→→↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓→→↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑¬↔𝜑𝜓Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓, 𝜒↗¬↔𝜑𝜓] into ax-2
3439→→↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑¬↔𝜑𝜓Modus ponens 3437, 3438
3440→↔𝜓¬𝜑¬↔𝜑𝜓Modus ponens 2894, 3439
3441→→¬↔𝜑𝜓↔𝜓¬𝜑→→↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into impbi
3442→→↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑Modus ponens 3430, 3441
3443↔¬↔𝜑𝜓↔𝜓¬𝜑Modus ponens 3440, 3442
3444→↔¬↔𝜑𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1
3445↔↔𝜓¬𝜑¬↔𝜑𝜓Modus ponens 3443, 3444
3446→↔↔𝜓¬𝜑↔¬𝜑𝜓↔↔¬𝜑𝜓↔𝜓¬𝜑Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓] into bicom1
3447→↔↔𝜓¬𝜑¬↔𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into biimp
3448→→↔𝜓¬𝜑¬↔𝜑𝜓→↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓Subs [𝜑↗→↔𝜓¬𝜑¬↔𝜑𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1
3449→↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓Modus ponens 3440, 3448
3450→→↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓→→↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓¬↔𝜑𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑, 𝜒↗¬↔𝜑𝜓] into ax-2
3451→→↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓¬↔𝜑𝜓Modus ponens 3449, 3450
3452→↔¬𝜑𝜓¬↔𝜑𝜓Modus ponens 2876, 3451
3453→↔↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into bicom1
3454→↔¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔𝜓¬𝜑Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into biimp
3455→→↔𝜓¬𝜑↔¬𝜑𝜓→¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓Subs [𝜑↗→↔𝜓¬𝜑↔¬𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
3456→¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓Modus ponens 2886, 3455
3457→→¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓→→¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔¬𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑, 𝜒↗↔¬𝜑𝜓] into ax-2
3458→→¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔¬𝜑𝜓Modus ponens 3456, 3457
3459→¬↔𝜑𝜓↔¬𝜑𝜓Modus ponens 3430, 3458
3460→→↔¬𝜑𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓¬↔𝜑𝜓Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into impbi
3461→→¬↔𝜑𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓¬↔𝜑𝜓Modus ponens 3452, 3460
3462↔↔¬𝜑𝜓¬↔𝜑𝜓Modus ponens 3459, 3461nbbn
3463→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓] into id
3464→↔→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into ax-1
3465→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens ibib, 3464
3466↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into pm5.74
3467→↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp
3468→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Modus ponens 3466, 3467
3469↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Modus ponens 3463, 3468
3470↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74
3471→↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3472→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3470, 3471
3473↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3465, 3472
3474→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3475→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3473, 3474
3476→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp
3477→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Modus ponens 3469, 3476
3478→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into ax-1
3479→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3475, 3478
3480→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into ax-2
3481→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3479, 3480
3482→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3477, 3481
3483→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into bicom1
3484↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Modus ponens 3473, 3483
3485→↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp
3486→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓Modus ponens 3484, 3485
3487→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into bicom1
3488↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Modus ponens 3469, 3487
3489→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into biimp
3490→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Modus ponens 3488, 3489
3491→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into ax-1
3492→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Modus ponens 3490, 3491
3493→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into ax-2
3494→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Modus ponens 3492, 3493
3495→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒Modus ponens 3486, 3494
3496→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into impbi
3497→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3482, 3496
3498↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3495, 3497
3499↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74
3500→↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into bicom1
3501↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Modus ponens 3499, 3500
3502→↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Subs [𝜑↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp
3503→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Modus ponens 3501, 3502
3504→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Modus ponens 3498, 3503
3505→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into id
3506→↔→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗↔→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into ax-1
3507→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3093, 3506
3508↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74
3509→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3510→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3508, 3509
3511↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3505, 3510
3512↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑𝜓] into pm5.74
3513→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into biimp
3514→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3512, 3513
3515↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3507, 3514
3516→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into biimp
3517→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3515, 3516
3518→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3519→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3511, 3518
3520→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into ax-1
3521→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3517, 3520
3522→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into ax-2
3523→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3521, 3522
3524→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3519, 3523
3525→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into bicom1
3526↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3515, 3525
3527→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3528→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 3526, 3527
3529→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into bicom1
3530↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Modus ponens 3511, 3529
3531→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into biimp
3532→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Modus ponens 3530, 3531
3533→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Subs [𝜑↗→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into ax-1
3534→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Modus ponens 3532, 3533
3535→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into ax-2
3536→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Modus ponens 3534, 3535
3537→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒Modus ponens 3528, 3536
3538→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into impbi
3539→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3524, 3538
3540↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Modus ponens 3537, 3539
3541↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into pm5.74
3542→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into bicom1
3543↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3541, 3542
3544→↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓] into biimp
3545→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3543, 3544
3546→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3540, 3545
3547→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into impbi
3548→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Modus ponens 3504, 3547
3549↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Modus ponens 3546, 3548
3550↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜓↗𝜒, 𝜒↗𝜓] into pm5.74
3551↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Subs [𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
3552→↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into bicom1
3553↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3551, 3552
3554→↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3555→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3553, 3554
3556→↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp
3557→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into ax-1
3558→↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3555, 3557
3559→→↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2
3560→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3558, 3559
3561→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3504, 3560
3562→↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1
3563→↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp
3564→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓Modus ponens 3551, 3563
3565→↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into bicom1
3566↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3549, 3565
3567→↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp
3568→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1
3569→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3546, 3568
3570→→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜒↗↔→𝜑𝜒→𝜑𝜓] into ax-2
3571→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3569, 3570
3572→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3564, 3571
3573→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi
3574→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3561, 3573
3575↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3572, 3574
3576→↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3577→↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp
3578→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3550, 3577
3579→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into ax-1
3580→→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3561, 3579
3581→→→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2
3582→→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3580, 3581
3583→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3578, 3582
3584→↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1
3585↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Modus ponens 3575, 3584
3586→↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp
3587→↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into bicom1
3588↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓Modus ponens 3550, 3587
3589→↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into biimp
3590→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓Modus ponens 3588, 3589
3591→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1
3592→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓Modus ponens 3590, 3591
3593→→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑↔𝜒𝜓] into ax-2
3594→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓Modus ponens 3592, 3593
3595→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓Modus ponens 3572, 3594
3596→→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi
3597→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3583, 3596
3598↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3595, 3597
3599↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜓↗↔𝜒𝜓, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74
3600→↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓] into bicom1
3601↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓Modus ponens 3599, 3600
3602→↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓Subs [𝜑↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓] into biimp
3603→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓Modus ponens 3601, 3602
3604→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓Modus ponens 3598, 3603
3605↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into bicom
3606→↔↔𝜓𝜒↔𝜒𝜓→𝜑↔↔𝜓𝜒↔𝜒𝜓Subs [𝜑↗↔↔𝜓𝜒↔𝜒𝜓, 𝜓↗𝜑] into ax-1
3607→𝜑↔↔𝜓𝜒↔𝜒𝜓Modus ponens 2677, 3606
3608↔→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜒𝜓] into pm5.74
3609→↔→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓] into biimp
3610→→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓Modus ponens 3608, 3609
3611↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓Modus ponens 3607, 3610
3612→↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓] into biimp
3613→→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3599, 3612
3614→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3615→↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓] into biimp
3616→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓Modus ponens 3611, 3615
3617→→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
3618→→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓Modus ponens 3583, 3617
3619→→→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2
3620→→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Modus ponens 3618, 3619
3621→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Modus ponens 3616, 3620
3622→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1
3623↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓Modus ponens 3598, 3622
3624→↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into biimp
3625→↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓] into bicom1
3626↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒Modus ponens 3611, 3625
3627→↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜓𝜒] into biimp
3628→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒Modus ponens 3626, 3627
3629→→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒Subs [𝜑↗→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1
3630→→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒Modus ponens 3628, 3629
3631→→→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
3632→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒Modus ponens 3630, 3631
3633→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒Modus ponens 3595, 3632
3634→→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi
3635→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Modus ponens 3621, 3634
3636↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Modus ponens 3633, 3635
3637↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74
3638→↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓] into bicom1
3639↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓Modus ponens 3637, 3638
3640→↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓] into biimp
3641→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓Modus ponens 3639, 3640
3642→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓Modus ponens 3636, 3641
3643→↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into bicom1
3644↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Modus ponens 3605, 3643
3645→↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Subs [𝜑↗↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
3646→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Modus ponens 3644, 3645
3647→↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓] into biimp
3648→→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Modus ponens 3637, 3647
3649↔→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒Subs [𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3650→↔→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒] into biimp
3651→→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒Modus ponens 3649, 3650
3652↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒Modus ponens 3646, 3651
3653→↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into biimp
3654→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒Modus ponens 3652, 3653
3655→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3656→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
3657→→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒Modus ponens 3654, 3656
3658→→→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓, 𝜒↗→𝜑↔↔𝜑𝜓𝜒] into ax-2
3659→→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Modus ponens 3657, 3658
3660→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Modus ponens 3621, 3659
3661→↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into bicom1
3662↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Modus ponens 3652, 3661
3663→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3664→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓Modus ponens 3662, 3663
3665→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1
3666↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒Modus ponens 3636, 3665
3667→↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into biimp
3668→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒Subs [𝜑↗→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into ax-1
3669→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒Modus ponens 3633, 3668
3670→→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
3671→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 3669, 3670
3672→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 3664, 3671
3673→→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into impbi
3674→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Modus ponens 3660, 3673
3675↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Modus ponens 3672, 3674
3676↔→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3677→↔→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒] into bicom1
3678↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3676, 3677
3679→↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒] into biimp
3680→↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3678, 3679
3681→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3675, 3680
3682→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜓↗↔𝜓𝜒] into pm5.501
3683↔↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into bicom
3684→↔↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒Subs [𝜑↗↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜓𝜒] into biimp
3685→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒Modus ponens 3683, 3684
3686→→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒Subs [𝜑↗→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒, 𝜓↗𝜑] into ax-1
3687→𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒Modus ponens 3685, 3686
3688→→𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒Subs [𝜓↗↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜒↗↔↔↔𝜑𝜓𝜒↔𝜓𝜒] into ax-2
3689→→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒Modus ponens 3687, 3688
3690→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒Modus ponens 3681, 3689
3691↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜓𝜒] into pm5.74
3692→↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒, 𝜓↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒] into biimp
3693→→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 3691, 3692
3694↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 3690, 3693
3695↔→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74
3696→↔→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒] into biimp
3697→→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Modus ponens 3695, 3696
3698↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Modus ponens 3682, 3697
3699→↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into biimp
3700→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Modus ponens 3698, 3699
3701→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
3702→→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into ax-1
3703→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Modus ponens 3700, 3702
3704→→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→𝜑↔𝜑↔𝜓𝜒] into ax-2
3705→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Modus ponens 3703, 3704
3706→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Modus ponens 3672, 3705
3707→↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into bicom1
3708↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 3698, 3707
3709→↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
3710→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 3708, 3709
3711→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into bicom1
3712→↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into biimp
3713→→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into ax-1
3714→→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Modus ponens 3660, 3713
3715→→→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→𝜑↔↔𝜑𝜓𝜒] into ax-2
3716→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Modus ponens 3714, 3715
3717→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒Modus ponens 3710, 3716
3718→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into impbi
3719→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Modus ponens 3706, 3718
3720↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Modus ponens 3717, 3719
3721↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒Subs [𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74
3722→↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒] into bicom1
3723↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 3721, 3722
3724→↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into biimp
3725→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 3723, 3724
3726→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 3720, 3725
3727↔↔¬𝜓𝜒¬↔𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into nbbn
3728→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into id
3729→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-1
3730→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3149, 3729
3731↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑¬𝜓] into pm5.74
3732→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp
3733→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3731, 3732
3734↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3728, 3733
3735↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74
3736→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp
3737→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3735, 3736
3738↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3730, 3737
3739→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp
3740→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3738, 3739
3741→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp
3742→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3734, 3741
3743→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into ax-1
3744→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3740, 3743
3745→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into ax-2
3746→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3744, 3745
3747→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3742, 3746
3748→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1
3749↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3738, 3748
3750→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp
3751→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓Modus ponens 3749, 3750
3752→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into bicom1
3753↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Modus ponens 3734, 3752
3754→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into biimp
3755→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Modus ponens 3753, 3754
3756→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into ax-1
3757→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Modus ponens 3755, 3756
3758→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into ax-2
3759→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Modus ponens 3757, 3758
3760→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒Modus ponens 3751, 3759
3761→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into impbi
3762→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3747, 3761
3763↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3760, 3762
3764↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74
3765→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1
3766↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Modus ponens 3764, 3765
3767→↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp
3768→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Modus ponens 3766, 3767
3769→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Modus ponens 3763, 3768
3770→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into id
3771→↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into ax-1
3772→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3319, 3771
3773↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74
3774→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp
3775→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Modus ponens 3773, 3774
3776↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Modus ponens 3770, 3775
3777↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜑𝜓, 𝜒↗→¬𝜑¬𝜓] into pm5.74
3778→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into biimp
3779→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3777, 3778
3780↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3772, 3779
3781→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into biimp
3782→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3780, 3781
3783→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp
3784→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Modus ponens 3776, 3783
3785→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into ax-1
3786→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3782, 3785
3787→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into ax-2
3788→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3786, 3787
3789→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3784, 3788
3790→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into bicom1
3791↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Modus ponens 3780, 3790
3792→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp
3793→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓Modus ponens 3791, 3792
3794→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into bicom1
3795↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Modus ponens 3776, 3794
3796→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into biimp
3797→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Modus ponens 3795, 3796
3798→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into ax-1
3799→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Modus ponens 3797, 3798
3800→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into ax-2
3801→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Modus ponens 3799, 3800
3802→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒Modus ponens 3793, 3801
3803→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into impbi
3804→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3789, 3803
3805↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Modus ponens 3802, 3804
3806↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑¬𝜓] into pm5.74
3807→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into bicom1
3808↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3806, 3807
3809→↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp
3810→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3808, 3809
3811→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3805, 3810
3812→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into impbi
3813→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Modus ponens 3769, 3812
3814↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Modus ponens 3811, 3813
3815↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗𝜒, 𝜒↗¬𝜓] into pm5.74
3816↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
3817→↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into bicom1
3818↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3816, 3817
3819→↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3820→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3818, 3819
3821→↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp
3822→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-1
3823→↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3820, 3822
3824→→↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2
3825→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3823, 3824
3826→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3769, 3825
3827→↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3828→↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp
3829→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓Modus ponens 3816, 3828
3830→↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into bicom1
3831↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3814, 3830
3832→↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp
3833→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1
3834→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3811, 3833
3835→→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜒↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-2
3836→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3834, 3835
3837→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3829, 3836
3838→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi
3839→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3826, 3838
3840↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3837, 3839
3841→↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3842→↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp
3843→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3815, 3842
3844→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into ax-1
3845→→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3826, 3844
3846→→→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2
3847→→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3845, 3846
3848→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3843, 3847
3849→↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3850↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Modus ponens 3840, 3849
3851→↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp
3852→↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into bicom1
3853↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓Modus ponens 3815, 3852
3854→↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp
3855→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓Modus ponens 3853, 3854
3856→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1
3857→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓Modus ponens 3855, 3856
3858→→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜒¬𝜓] into ax-2
3859→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓Modus ponens 3857, 3858
3860→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓Modus ponens 3837, 3859
3861→→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi
3862→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3848, 3861
3863↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3860, 3862
3864↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔𝜒¬𝜓, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74
3865→↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3866↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓Modus ponens 3864, 3865
3867→↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓Subs [𝜑↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓] into biimp
3868→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓Modus ponens 3866, 3867
3869→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓Modus ponens 3863, 3868
3870↔↔¬𝜓𝜒↔𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗𝜒] into bicom
3871→↔↔¬𝜓𝜒↔𝜒¬𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓Subs [𝜑↗↔↔¬𝜓𝜒↔𝜒¬𝜓, 𝜓↗¬𝜑] into ax-1
3872→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓Modus ponens 3870, 3871
3873↔→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔𝜒¬𝜓] into pm5.74
3874→↔→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓] into biimp
3875→→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓Modus ponens 3873, 3874
3876↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓Modus ponens 3872, 3875
3877→↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3878→→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3864, 3877
3879→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3880→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp
3881→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓Modus ponens 3876, 3880
3882→→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into ax-1
3883→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3848, 3882
3884→→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2
3885→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3883, 3884
3886→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3881, 3885
3887→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3888↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓Modus ponens 3863, 3887
3889→↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp
3890→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓] into bicom1
3891↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒Modus ponens 3876, 3890
3892→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp
3893→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒Modus ponens 3891, 3892
3894→→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1
3895→→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒Modus ponens 3893, 3894
3896→→→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓, 𝜒↗→¬𝜑↔¬𝜓𝜒] into ax-2
3897→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒Modus ponens 3895, 3896
3898→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒Modus ponens 3860, 3897
3899→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi
3900→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3886, 3899
3901↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3898, 3900
3902↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74
3903→↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3904↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓Modus ponens 3902, 3903
3905→↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓] into biimp
3906→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓Modus ponens 3904, 3905
3907→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓Modus ponens 3901, 3906
3908→↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Subs [𝜑↗↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗¬𝜑] into ax-1
3909→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Modus ponens 3644, 3908
3910→↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3911→→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3902, 3910
3912↔→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3913→↔→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒] into biimp
3914→→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3912, 3913
3915↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3909, 3914
3916→↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp
3917→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3915, 3916
3918→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3919→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into ax-1
3920→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3917, 3919
3921→→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2
3922→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3920, 3921
3923→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3886, 3922
3924→↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into bicom1
3925↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3915, 3924
3926→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3927→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓Modus ponens 3925, 3926
3928→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3929↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒Modus ponens 3901, 3928
3930→↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp
3931→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1
3932→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒Modus ponens 3898, 3931
3933→→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜒↗→¬𝜑↔¬𝜓𝜒] into ax-2
3934→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒Modus ponens 3932, 3933
3935→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒Modus ponens 3927, 3934
3936→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into impbi
3937→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3923, 3936
3938↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3935, 3937
3939↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3940→↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into bicom1
3941↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3939, 3940
3942→↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒] into biimp
3943→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3941, 3942
3944→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3938, 3943
3945→↔↔¬𝜓𝜒¬↔𝜓𝜒↔¬↔𝜓𝜒↔¬𝜓𝜒Subs [𝜑↗↔¬𝜓𝜒, 𝜓↗¬↔𝜓𝜒] into bicom1
3946↔¬↔𝜓𝜒↔¬𝜓𝜒Modus ponens 3727, 3945
3947→↔¬↔𝜓𝜒↔¬𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒Subs [𝜑↗↔¬↔𝜓𝜒↔¬𝜓𝜒, 𝜓↗¬𝜑] into ax-1
3948→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒Modus ponens 3946, 3947
3949↔→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔¬𝜓𝜒] into pm5.74
3950→↔→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒] into biimp
3951→→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒Modus ponens 3949, 3950
3952↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒Modus ponens 3948, 3951
3953→↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into biimp
3954→→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3939, 3953
3955→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp
3956→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp
3957→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒Modus ponens 3952, 3956
3958→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into ax-1
3959→→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3923, 3958
3960→→→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2
3961→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3959, 3960
3962→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3957, 3961
3963→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into bicom1
3964↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒Modus ponens 3938, 3963
3965→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp
3966→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into bicom1
3967↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 3952, 3966
3968→↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp
3969→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 3967, 3968
3970→→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1
3971→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 3969, 3970
3972→→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒, 𝜒↗→¬𝜑¬↔𝜓𝜒] into ax-2
3973→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 3971, 3972
3974→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 3935, 3973
3975→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into impbi
3976→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3962, 3975
3977↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3974, 3976
3978↔→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3979→↔→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into bicom1
3980↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3978, 3979
3981→↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒] into biimp
3982→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3980, 3981
3983→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒Modus ponens 3977, 3982
3984→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜓↗↔𝜓𝜒] into nbn2
3985↔↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒Subs [𝜑↗¬↔𝜓𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into bicom
3986→↔↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒Subs [𝜑↗↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒] into biimp
3987→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒Modus ponens 3985, 3986
3988→→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒Subs [𝜑↗→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
3989→¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒Modus ponens 3987, 3988
3990→→¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜒↗↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒] into ax-2
3991→→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒Modus ponens 3989, 3990
3992→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒Modus ponens 3983, 3991
3993↔→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗¬↔𝜓𝜒] into pm5.74
3994→↔→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒, 𝜓↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒] into biimp
3995→→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 3993, 3994
3996↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 3992, 3995
3997↔→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74
3998→↔→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒] into biimp
3999→→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Modus ponens 3997, 3998
4000↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Modus ponens 3984, 3999
4001→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into biimp
4002→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Modus ponens 4000, 4001
4003→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp
4004→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1
4005→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Modus ponens 4002, 4004
4006→→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒, 𝜒↗→¬𝜑↔𝜑↔𝜓𝜒] into ax-2
4007→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Modus ponens 4005, 4006
4008→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Modus ponens 3974, 4007
4009→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into bicom1
4010↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 4000, 4009
4011→↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒Subs [𝜑↗→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp
4012→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒Modus ponens 4010, 4011
4013→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into bicom1
4014→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp
4015→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into ax-1
4016→→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 3962, 4015
4017→→→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Subs [𝜑↗→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2
4018→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 4016, 4017
4019→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒Modus ponens 4012, 4018
4020→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into impbi
4021→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Modus ponens 4008, 4020
4022↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Modus ponens 4019, 4021
4023↔→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74
4024→↔→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒] into bicom1
4025↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4023, 4024
4026→↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into biimp
4027→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4025, 4026
4028→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4022, 4027
4029→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into id
4030→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
4031→¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4029, 4030
4032→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into notnotr
4033→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
4034→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1
4035→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4033, 4034
4036→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4037→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4035, 4036
4038→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4032, 4037
4039→→¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4040→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4031, 4039
4041→→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1
4042→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4040, 4041
4043→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4044→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4042, 4043
4045→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1
4046→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1
4047→¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑Modus ponens 4045, 4046
4048→→¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑] into ax-2
4049→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑Modus ponens 4047, 4048
4050→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4051→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4038, 4050
4052→→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
4053→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4051, 4052
4054→→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑, 𝜒↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4055→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4053, 4054
4056→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4045, 4055
4057→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-3
4058→→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
4059→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4057, 4058
4060→→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4061→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4059, 4060
4062→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4056, 4061
4063→→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬𝜑, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4064→→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4062, 4063
4065→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4028, 4064
4066→→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑Subs [𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-3
4067→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑Modus ponens 4065, 4066
4068→→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1
4069→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 3726, 4068
4070→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗𝜑, 𝜒↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4071→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4069, 4070
4072→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4067, 4071
4073→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Subs [𝜑↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into pm2.18
4074↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒Modus ponens 4072, 4073biass
4075→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓Subs [𝜑↗↔𝜒↔𝜑𝜓] into id
4076→↔↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜒↔𝜑𝜓] into ax-1
4077→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑Modus ponens bicom, 4076
4078↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
4079→↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp
4080→→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓Modus ponens 4078, 4079
4081↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓Modus ponens 4075, 4080
4082↔→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into pm5.74
4083→↔→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑] into biimp
4084→→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑Modus ponens 4082, 4083
4085↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑Modus ponens 4077, 4084
4086→↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into biimp
4087→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑Modus ponens 4085, 4086
4088→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp
4089→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓Modus ponens 4081, 4088
4090→→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓𝜒] into ax-1
4091→→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑Modus ponens 4087, 4090
4092→→→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into ax-2
4093→→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑Modus ponens 4091, 4092
4094→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑Modus ponens 4089, 4093
4095→↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into bicom1
4096↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓Modus ponens 4085, 4095
4097→↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp
4098→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓Modus ponens 4096, 4097
4099→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into bicom1
4100↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒Modus ponens 4081, 4099
4101→↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓𝜒] into biimp
4102→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒Modus ponens 4100, 4101
4103→→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒Subs [𝜑↗→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into ax-1
4104→→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒Modus ponens 4102, 4103
4105→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜒↔𝜑𝜓𝜒] into ax-2
4106→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒Modus ponens 4104, 4105
4107→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒Modus ponens 4098, 4106
4108→→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into impbi
4109→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑Modus ponens 4094, 4108
4110↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑Modus ponens 4107, 4109
4111↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜓𝜑] into pm5.74
4112→↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑] into bicom1
4113↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Modus ponens 4111, 4112
4114→↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Subs [𝜑↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑] into biimp
4115→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Modus ponens 4113, 4114
4116→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Modus ponens 4110, 4115
4117→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑Subs [𝜑↗↔𝜒↔𝜓𝜑] into id
4118→↔↔𝜑𝜓↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into bicom1
4119→↔↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into ax-1
4120→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓Modus ponens 3157, 4119
4121↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗𝜒, 𝜒↗↔𝜓𝜑] into pm5.74
4122→↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp
4123→→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑Modus ponens 4121, 4122
4124↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑Modus ponens 4117, 4123
4125↔→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔𝜓𝜑, 𝜒↗↔𝜑𝜓] into pm5.74
4126→↔→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓] into biimp
4127→→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓Modus ponens 4125, 4126
4128↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓Modus ponens 4120, 4127
4129→↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into biimp
4130→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓Modus ponens 4128, 4129
4131→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp
4132→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑Modus ponens 4124, 4131
4133→→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑𝜒] into ax-1
4134→→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓Modus ponens 4130, 4133
4135→→→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜒↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into ax-2
4136→→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓Modus ponens 4134, 4135
4137→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓Modus ponens 4132, 4136
4138→↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into bicom1
4139↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑Modus ponens 4128, 4138
4140→↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp
4141→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑Modus ponens 4139, 4140
4142→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into bicom1
4143↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒Modus ponens 4124, 4142
4144→↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑𝜒] into biimp
4145→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒Modus ponens 4143, 4144
4146→→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒Subs [𝜑↗→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into ax-1
4147→→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒Modus ponens 4145, 4146
4148→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜒↗→↔𝜒↔𝜓𝜑𝜒] into ax-2
4149→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒Modus ponens 4147, 4148
4150→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒Modus ponens 4141, 4149
4151→→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into impbi
4152→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓Modus ponens 4137, 4151
4153↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓Modus ponens 4150, 4152
4154↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
4155→↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓] into bicom1
4156↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Modus ponens 4154, 4155
4157→↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓] into biimp
4158→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Modus ponens 4156, 4157
4159→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Modus ponens 4153, 4158
4160→→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into impbi
4161→→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Modus ponens 4116, 4160
4162↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Modus ponens 4159, 4161
4163↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗↔𝜓𝜑] into bicom
4164→↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔↔𝜓𝜑𝜒] into biimp
4165→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒Modus ponens 4163, 4164
4166→↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into biimp
4167→→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒Subs [𝜑↗→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into ax-1
4168→↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒Modus ponens 4165, 4167
4169→→↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑, 𝜒↗↔↔𝜓𝜑𝜒] into ax-2
4170→→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Modus ponens 4168, 4169
4171→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Modus ponens 4116, 4170
4172→↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1
4173↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑Modus ponens 4163, 4172
4174→↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜓𝜑] into biimp
4175→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑Modus ponens 4173, 4174
4176→↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into bicom1
4177↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Modus ponens 4162, 4176
4178→↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔𝜒↔𝜑𝜓] into biimp
4179→→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into ax-1
4180→↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓Modus ponens 4159, 4179
4181→→↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜓𝜑, 𝜒↗↔𝜒↔𝜑𝜓] into ax-2
4182→→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓Modus ponens 4180, 4181
4183→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓Modus ponens 4175, 4182
4184→→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into impbi
4185→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Modus ponens 4171, 4184
4186↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Modus ponens 4183, 4185
4187→↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into biimp
4188→↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into biimp
4189→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓Modus ponens 3605, 4188
4190→→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into ax-1
4191→↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒Modus ponens 4171, 4190
4192→→↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜓𝜑𝜒] into ax-2
4193→→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒Modus ponens 4191, 4192
4194→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒Modus ponens 4189, 4193
4195→↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1
4196↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓Modus ponens 4186, 4195
4197→↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into biimp
4198→↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓𝜒] into biimp
4199→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Modus ponens 3644, 4198
4200→→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into ax-1
4201→↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒Modus ponens 4199, 4200
4202→→↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into ax-2
4203→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒Modus ponens 4201, 4202
4204→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒Modus ponens 4183, 4203
4205→→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into impbi
4206→→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒Modus ponens 4194, 4205
4207↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒Modus ponens 4204, 4206
4208↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗𝜑] into biass
4209→↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into biimp
4210→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒Modus ponens 4208, 4209
4211→↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into biimp
4212→→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into ax-1
4213→↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒Modus ponens 4210, 4212
4214→→↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒, 𝜒↗↔𝜓↔𝜑𝜒] into ax-2
4215→→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒Modus ponens 4213, 4214
4216→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒Modus ponens 4194, 4215
4217→↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into bicom1
4218↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒Modus ponens 4208, 4217
4219→↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒Subs [𝜑↗↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into biimp
4220→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒Modus ponens 4218, 4219
4221→↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1
4222↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒Modus ponens 4207, 4221
4223→↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into biimp
4224→→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into ax-1
4225→↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒Modus ponens 4204, 4224
4226→→↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒Subs [𝜑↗↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜓𝜑𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into ax-2
4227→→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒Modus ponens 4225, 4226
4228→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒Modus ponens 4220, 4227
4229→→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒→→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into impbi
4230→→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒Modus ponens 4216, 4229
4231↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒Modus ponens 4228, 4230
4232↔↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜓↔𝜑𝜒] into biass
4233→↔↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒] into biimp
4234→↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒Modus ponens 4232, 4233
4235↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒Modus ponens 4231, 4234
4236↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗𝜒, 𝜒↗↔𝜑𝜒] into biass
4237→↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into bicom1
4238↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒Modus ponens 4236, 4237
4239→↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into biimp
4240→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒Modus ponens 4238, 4239
4241→↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into biimp
4242→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒Modus ponens 4235, 4241
4243→→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
4244→↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒Modus ponens 4240, 4243
4245→→↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒, 𝜒↗↔↔𝜒𝜓↔𝜑𝜒] into ax-2
4246→→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒Modus ponens 4244, 4245
4247→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒Modus ponens 4242, 4246
4248→↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into bicom1
4249→↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into biimp
4250→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒Modus ponens 4236, 4249
4251→↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into bicom1
4252↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓Modus ponens 4235, 4251
4253→↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into biimp
4254→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓Modus ponens 4252, 4253
4255→→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓Subs [𝜑↗→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into ax-1
4256→↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓Modus ponens 4254, 4255
4257→→↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒, 𝜒↗↔𝜑𝜓] into ax-2
4258→→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓Modus ponens 4256, 4257
4259→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓Modus ponens 4250, 4258
4260→→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒→→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into impbi
4261→→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒Modus ponens 4247, 4260
4262↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒Modus ponens 4259, 4261biluk
4263↔↔𝜑𝜑¬↔𝜑¬𝜑Subs [𝜓↗𝜑] into pm5.18
4264→↔↔𝜑𝜑¬↔𝜑¬𝜑→↔𝜑𝜑¬↔𝜑¬𝜑Subs [𝜑↗↔𝜑𝜑, 𝜓↗¬↔𝜑¬𝜑] into biimp
4265→↔𝜑𝜑¬↔𝜑¬𝜑Modus ponens 4263, 4264
4266¬↔𝜑¬𝜑Modus ponens biid, 4265pm5.19
4267→→𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm2.04
4268→→→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→𝜑𝜒] into impbi
4269→→→𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒Modus ponens pm2.04, 4268
4270↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒Modus ponens 4267, 4269bi2.04
4271↔→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓Subs [𝜓↗→𝜑𝜓, 𝜒↗𝜓] into pm5.74
4272→↔→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓→→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑↔→𝜑𝜓𝜓, 𝜓↗↔→𝜑→𝜑𝜓→𝜑𝜓] into biimp
4273→→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓Modus ponens 4271, 4272
4274↔→𝜑→𝜑𝜓→𝜑𝜓Modus ponens pm5.5, 4273pm5.4
4275→→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into impbi
4276→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens ax-2, 4275
4277↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens pm2.86, 4276imdi
4278→↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into bicom1
4279↔→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒Modus ponens imdi, 4278pm5.41
4280→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imbi2
4281→↔→𝜑→𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑→𝜑𝜓Subs [𝜑↗→𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1
4282↔→𝜑𝜓→𝜑→𝜑𝜓Modus ponens pm5.4, 4281
4283→↔→𝜑𝜓→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗↔→𝜑𝜓𝜒] into ax-1
4284→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓Modus ponens 4282, 4283
4285↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into pm5.74
4286→↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp
4287→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Modus ponens 4285, 4286
4288↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Modus ponens 4284, 4287
4289↔→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑𝜒] into pm5.74
4290→↔→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒] into biimp
4291→→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Modus ponens 4289, 4290
4292↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Modus ponens 4280, 4291
4293→↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into biimp
4294→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Modus ponens 4292, 4293
4295→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp
4296→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Modus ponens 4288, 4295
4297→→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Subs [𝜑↗→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜓] into ax-1
4298→→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Modus ponens 4294, 4297
4299→→→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓𝜒→𝜑𝜒] into ax-2
4300→→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Modus ponens 4298, 4299
4301→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Modus ponens 4296, 4300
4302→↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into bicom1
4303↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Modus ponens 4292, 4302
4304→↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp
4305→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓Modus ponens 4303, 4304
4306→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into bicom1
4307↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓Modus ponens 4288, 4306
4308→↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜓] into biimp
4309→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓Modus ponens 4307, 4308
4310→→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into ax-1
4311→→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓Modus ponens 4309, 4310
4312→→→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓𝜒→𝜑𝜓] into ax-2
4313→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓Modus ponens 4311, 4312
4314→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓Modus ponens 4305, 4313
4315→→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into impbi
4316→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Modus ponens 4301, 4315
4317↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Modus ponens 4314, 4316
4318↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into pm5.74
4319→↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒] into bicom1
4320↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 4318, 4319
4321→↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into biimp
4322→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 4320, 4321
4323→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒Modus ponens 4317, 4322
4324→↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into bicom1
4325↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Modus ponens pm5.74, 4324
4326→↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
4327→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓𝜒] into ax-1
4328→↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Modus ponens 1905, 4327
4329→→↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
4330→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 4328, 4329
4331→↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒Modus ponens 4323, 4330imbibi
4332→→→𝜑¬𝜑¬𝜑→→¬𝜑→𝜑¬𝜑↔→𝜑¬𝜑¬𝜑Subs [𝜑↗→𝜑¬𝜑, 𝜓↗¬𝜑] into impbi
4333→→¬𝜑→𝜑¬𝜑↔→𝜑¬𝜑¬𝜑Modus ponens pm2.01, 4332
4334↔→𝜑¬𝜑¬𝜑Modus ponens 414, 4333pm4.8
4335→→→¬𝜑𝜑𝜑→→𝜑→¬𝜑𝜑↔→¬𝜑𝜑𝜑Subs [𝜑↗→¬𝜑𝜑, 𝜓↗𝜑] into impbi
4336→→𝜑→¬𝜑𝜑↔→¬𝜑𝜑𝜑Modus ponens pm2.18, 4335
4337↔→¬𝜑𝜑𝜑Modus ponens 322, 4336pm4.81
4338↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜒, 𝜒↗𝜃] into bi2.04
4339→𝜑↔→𝜑𝜒𝜒Subs [𝜓↗𝜒] into pm5.5
4340↔↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒] into bicom
4341→↔↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒Subs [𝜑↗↔→𝜑𝜒𝜒, 𝜓↗↔𝜒→𝜑𝜒] into biimp
4342→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒Modus ponens 4340, 4341
4343→→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4344→𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒Modus ponens 4342, 4343
4345→→𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→→𝜑↔→𝜑𝜒𝜒→𝜑↔𝜒→𝜑𝜒Subs [𝜓↗↔→𝜑𝜒𝜒, 𝜒↗↔𝜒→𝜑𝜒] into ax-2
4346→→𝜑↔→𝜑𝜒𝜒→𝜑↔𝜒→𝜑𝜒Modus ponens 4344, 4345
4347→𝜑↔𝜒→𝜑𝜒Modus ponens 4339, 4346
4348→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒] into biimp
4349→→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒→𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒Subs [𝜑↗→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4350→𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒Modus ponens 4348, 4349
4351→→𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒→→𝜑↔𝜒→𝜑𝜒→𝜑→𝜒→𝜑𝜒Subs [𝜓↗↔𝜒→𝜑𝜒, 𝜒↗→𝜒→𝜑𝜒] into ax-2
4352→→𝜑↔𝜒→𝜑𝜒→𝜑→𝜒→𝜑𝜒Modus ponens 4350, 4351
4353→𝜑→𝜒→𝜑𝜒Modus ponens 4347, 4352
4354→→𝜒→𝜑𝜒→𝜒→𝜒→𝜑𝜒Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗𝜒] into ax-1
4355→𝜒→𝜒→𝜑𝜒Modus ponens 1834, 4354
4356→→𝜒→𝜒→𝜑𝜒→→𝜒𝜒→𝜒→𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
4357→→𝜒𝜒→𝜒→𝜑𝜒Modus ponens 4355, 4356
4358→→𝜑→𝜒→𝜑𝜒→→𝜑𝜒→𝜑→𝜑𝜒Subs [𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
4359→→𝜑𝜒→𝜑→𝜑𝜒Modus ponens 4353, 4358
4360→→→𝜑𝜒→𝜑→𝜑𝜒→𝜒→→𝜑𝜒→𝜑→𝜑𝜒Subs [𝜑↗→→𝜑𝜒→𝜑→𝜑𝜒, 𝜓↗𝜒] into ax-1
4361→𝜒→→𝜑𝜒→𝜑→𝜑𝜒Modus ponens 4359, 4360
4362→→𝜒→→𝜑𝜒→𝜑→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→𝜑→𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→𝜑𝜒] into ax-2
4363→→𝜒→𝜑𝜒→𝜒→𝜑→𝜑𝜒Modus ponens 4361, 4362
4364→𝜒→𝜑→𝜑𝜒Modus ponens 1834, 4363
4365→→𝜒→𝜑→𝜑𝜒→→𝜒𝜑→𝜒→𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗→𝜑𝜒] into ax-2
4366→→𝜒𝜑→𝜒→𝜑𝜒Modus ponens 4364, 4365
4367→→→𝜒𝜑→𝜒→𝜑𝜒→𝜑→→𝜒𝜑→𝜒→𝜑𝜒Subs [𝜑↗→→𝜒𝜑→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4368→𝜑→→𝜒𝜑→𝜒→𝜑𝜒Modus ponens 4366, 4367
4369→→𝜑→→𝜒𝜑→𝜒→𝜑𝜒→→𝜑→𝜒𝜑→𝜑→𝜒→𝜑𝜒Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜒→𝜑𝜒] into ax-2
4370→→𝜑→𝜒𝜑→𝜑→𝜒→𝜑𝜒Modus ponens 4368, 4369
4371→𝜑→𝜃𝜃Subs [𝜓↗𝜃] into idd
4372→→𝜃𝜃→→𝜑𝜒→𝜃𝜃Subs [𝜑↗→𝜃𝜃, 𝜓↗→𝜑𝜒] into ax-1
4373→→→𝜃𝜃→→𝜑𝜒→𝜃𝜃→𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃Subs [𝜑↗→→𝜃𝜃→→𝜑𝜒→𝜃𝜃, 𝜓↗𝜑] into ax-1
4374→𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃Modus ponens 4372, 4373
4375→→𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃→→𝜑→𝜃𝜃→𝜑→→𝜑𝜒→𝜃𝜃Subs [𝜓↗→𝜃𝜃, 𝜒↗→→𝜑𝜒→𝜃𝜃] into ax-2
4376→→𝜑→𝜃𝜃→𝜑→→𝜑𝜒→𝜃𝜃Modus ponens 4374, 4375
4377→𝜑→→𝜑𝜒→𝜃𝜃Modus ponens 4371, 4376
4378→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜃, 𝜒↗𝜃] into ax-2
4379→→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃Subs [𝜑↗→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1
4380→𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4378, 4379
4381→→𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜑𝜒→𝜃𝜃→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃Subs [𝜓↗→→𝜑𝜒→𝜃𝜃, 𝜒↗→→→𝜑𝜒𝜃→→𝜑𝜒𝜃] into ax-2
4382→→𝜑→→𝜑𝜒→𝜃𝜃→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4380, 4381
4383→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4377, 4382
4384→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗→→𝜑𝜒𝜃] into ax-1
4385→→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒Subs [𝜑↗→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4386→𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒Modus ponens 4384, 4385
4387→→𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→𝜑→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒Subs [𝜓↗→𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒𝜃→𝜒→𝜑𝜒] into ax-2
4388→→𝜑→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒Modus ponens 4386, 4387
4389→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒Modus ponens 4353, 4388
4390→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜃] into imim2
4391→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Subs [𝜑↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜓↗→→𝜑𝜒𝜃] into ax-1
4392→→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Modus ponens 4390, 4391
4393→→→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→→𝜑𝜒𝜃, 𝜒↗→→𝜒→𝜑𝜒→𝜒𝜃] into ax-2
4394→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Modus ponens 4392, 4393
4395→→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Subs [𝜑↗→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜓↗𝜑] into ax-1
4396→𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Modus ponens 4394, 4395
4397→→𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Subs [𝜓↗→→→𝜑𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃] into ax-2
4398→→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Modus ponens 4396, 4397
4399→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃Modus ponens 4383, 4398
4400→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→𝜒→𝜑𝜒, 𝜒↗→𝜒𝜃] into ax-2
4401→→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4402→𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4400, 4401
4403→→𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜓↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4404→→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4402, 4403
4405→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4399, 4404
4406→→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4407→→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4405, 4406
4408→𝜑→→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4389, 4407
4409→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒] into biimp
4410→→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒→𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒Subs [𝜑↗→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒, 𝜓↗𝜑] into ax-1
4411→𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒Modus ponens 4409, 4410
4412→→𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒→→𝜑↔→𝜑𝜒𝜒→𝜑→→𝜑𝜒𝜒Subs [𝜓↗↔→𝜑𝜒𝜒, 𝜒↗→→𝜑𝜒𝜒] into ax-2
4413→→𝜑↔→𝜑𝜒𝜒→𝜑→→𝜑𝜒𝜒Modus ponens 4411, 4412
4414→→𝜃𝜃→𝜒→𝜃𝜃Subs [𝜑↗→𝜃𝜃, 𝜓↗𝜒] into ax-1
4415→→→𝜃𝜃→𝜒→𝜃𝜃→𝜑→→𝜃𝜃→𝜒→𝜃𝜃Subs [𝜑↗→→𝜃𝜃→𝜒→𝜃𝜃, 𝜓↗𝜑] into ax-1
4416→𝜑→→𝜃𝜃→𝜒→𝜃𝜃Modus ponens 4414, 4415
4417→→𝜑→→𝜃𝜃→𝜒→𝜃𝜃→→𝜑→𝜃𝜃→𝜑→𝜒→𝜃𝜃Subs [𝜓↗→𝜃𝜃, 𝜒↗→𝜒→𝜃𝜃] into ax-2
4418→→𝜑→𝜃𝜃→𝜑→𝜒→𝜃𝜃Modus ponens 4416, 4417
4419→𝜑→𝜒→𝜃𝜃Modus ponens 4371, 4418
4420→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗𝜃] into ax-2
4421→→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃Subs [𝜑↗→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4422→𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃Modus ponens 4420, 4421
4423→→𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃→→𝜑→𝜒→𝜃𝜃→𝜑→→𝜒𝜃→𝜒𝜃Subs [𝜓↗→𝜒→𝜃𝜃, 𝜒↗→→𝜒𝜃→𝜒𝜃] into ax-2
4424→→𝜑→𝜒→𝜃𝜃→𝜑→→𝜒𝜃→𝜒𝜃Modus ponens 4422, 4423
4425→𝜑→→𝜒𝜃→𝜒𝜃Modus ponens 4419, 4424
4426→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒Subs [𝜑↗→→𝜑𝜒𝜒, 𝜓↗→𝜒𝜃] into ax-1
4427→→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒Subs [𝜑↗→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒, 𝜓↗𝜑] into ax-1
4428→𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒Modus ponens 4426, 4427
4429→→𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜒Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜒𝜃→→𝜑𝜒𝜒] into ax-2
4430→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜒Modus ponens 4428, 4429
4431→𝜑→→𝜒𝜃→→𝜑𝜒𝜒Modus ponens 264, 4430
4432→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗→𝜑𝜒] into imim2
4433→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Subs [𝜑↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
4434→→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Modus ponens 4432, 4433
4435→→→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→→→𝜑𝜒𝜒→→𝜑𝜒𝜃] into ax-2
4436→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Modus ponens 4434, 4435
4437→→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Subs [𝜑↗→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1
4438→𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Modus ponens 4436, 4437
4439→→𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Subs [𝜓↗→→𝜒𝜃→𝜒𝜃, 𝜒↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃] into ax-2
4440→→𝜑→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Modus ponens 4438, 4439
4441→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃Modus ponens 4425, 4440
4442→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜑𝜒𝜃] into ax-2
4443→→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃Subs [𝜑↗→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1
4444→𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4442, 4443
4445→→𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃Subs [𝜓↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜒↗→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2
4446→→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4444, 4445
4447→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4441, 4446
4448→→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜃Subs [𝜓↗→→𝜒𝜃→→𝜑𝜒𝜒, 𝜒↗→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2
4449→→𝜑→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4447, 4448
4450→𝜑→→𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4431, 4449
4451→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into impbi
4452→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃Subs [𝜑↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1
4453→→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃Subs [𝜑↗→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1
4454→𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4452, 4453
4455→→𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃Subs [𝜓↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2
4456→→𝜑→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4454, 4455
4457→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃Modus ponens 4450, 4456
4458→→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4459→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4451, 4458
4460→→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4461→𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4459, 4460
4462→→𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜓↗→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4463→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4461, 4462
4464→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4457, 4463
4465→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃] into id
4466→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4467→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1
4468→→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4466, 4467
4469→→→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4470→→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4468, 4469
4471→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4472→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4464, 4471
4473→→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1
4474→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4472, 4473
4475→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→𝜑→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4476→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4474, 4475
4477→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4466, 4476
4478→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4479→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4477, 4478
4480→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4481→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4479, 4480
4482→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4408, 4481
4483→→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜓↗𝜑, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4484→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4482, 4483
4485→→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4486→𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4484, 4485
4487→→𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→𝜑𝜑→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4488→→𝜑→𝜑𝜑→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4486, 4487
4489→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens id, 4484
4490→→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-1
4491→𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4489, 4490
4492→→𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4493→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃Modus ponens 4491, 4492
4494↔→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜒𝜃, 𝜒↗→𝜒𝜃] into pm5.74
4495→↔→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃Subs [𝜑↗→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃] into biimp
4496→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃Modus ponens 4494, 4495
4497→→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃Subs [𝜑↗→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃, 𝜓↗→𝜓𝜑] into ax-1
4498→→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃Modus ponens 4496, 4497
4499→→→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃] into ax-2
4500→→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃Modus ponens 4498, 4499
4501→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃Modus ponens 4493, 4500
4502→↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃Subs [𝜑↗↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃, 𝜓↗→𝜓𝜑] into ax-1
4503→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃Modus ponens 4338, 4502
4504↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜒→𝜓𝜃, 𝜒↗→𝜓→→𝜑𝜒𝜃] into pm5.74
4505→↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Subs [𝜑↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃, 𝜓↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp
4506→→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Modus ponens 4504, 4505
4507↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Modus ponens 4503, 4506
4508↔→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓→→𝜑𝜒𝜃, 𝜒↗→𝜓→𝜒𝜃] into pm5.74
4509→↔→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃Subs [𝜑↗→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃, 𝜓↗↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃] into biimp
4510→→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃Modus ponens 4508, 4509
4511↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃Modus ponens 4501, 4510
4512→↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into biimp
4513→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃Modus ponens 4511, 4512
4514→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp
4515→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Modus ponens 4507, 4514
4516→→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃Subs [𝜑↗→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into ax-1
4517→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃Modus ponens 4513, 4516
4518→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜒↗→→𝜓𝜑→𝜓→𝜒𝜃] into ax-2
4519→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃Modus ponens 4517, 4518
4520→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃Modus ponens 4515, 4519
4521→↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into bicom1
4522↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Modus ponens 4511, 4521
4523→↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp
4524→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃Modus ponens 4522, 4523
4525→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into bicom1
4526↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Modus ponens 4507, 4525
4527→↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into biimp
4528→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Modus ponens 4526, 4527
4529→→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Subs [𝜑↗→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into ax-1
4530→→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Modus ponens 4528, 4529
4531→→→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜒↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into ax-2
4532→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Modus ponens 4530, 4531
4533→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃Modus ponens 4524, 4532
4534→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into impbi
4535→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃Modus ponens 4520, 4534
4536↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃Modus ponens 4533, 4535
4537↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜒→𝜓𝜃, 𝜒↗→𝜓→𝜒𝜃] into pm5.74
4538→↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃Subs [𝜑↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃, 𝜓↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃] into bicom1
4539↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃Modus ponens 4537, 4538
4540→↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃Subs [𝜑↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃] into biimp
4541→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃Modus ponens 4539, 4540
4542→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃Modus ponens 4536, 4541imim21b
4543→↔⋀𝜑𝜓¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into bicom1
4544↔¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens df-an, 4543pm4.63
4545↔¬→¬𝜑¬𝜓⋀¬𝜑𝜓Subs [𝜑↗¬𝜑] into pm4.63pm4.67
4546↔→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓] into notnotb
4547↔↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓] into notbi
4548→↔↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓→↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓] into biimp
4549→↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓Modus ponens 4547, 4548
4550↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓Modus ponens pm4.63, 4549
4551→↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into biimp
4552→¬¬→𝜑¬𝜓¬⋀𝜑𝜓Modus ponens 4550, 4551
4553→↔→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into biimp
4554→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 4546, 4553
4555→→¬¬→𝜑¬𝜓¬⋀𝜑𝜓→→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓Subs [𝜑↗→¬¬→𝜑¬𝜓¬⋀𝜑𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
4556→→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓Modus ponens 4552, 4555
4557→→→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓→→→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬⋀𝜑𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓, 𝜒↗¬⋀𝜑𝜓] into ax-2
4558→→→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬⋀𝜑𝜓Modus ponens 4556, 4557
4559→→𝜑¬𝜓¬⋀𝜑𝜓Modus ponens 4554, 4558
4560→↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into bicom1
4561↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓Modus ponens 4550, 4560
4562→↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬¬→𝜑¬𝜓] into biimp
4563→¬⋀𝜑𝜓¬¬→𝜑¬𝜓Modus ponens 4561, 4562
4564→↔→𝜑¬𝜓¬¬→𝜑¬𝜓↔¬¬→𝜑¬𝜓→𝜑¬𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into bicom1
4565↔¬¬→𝜑¬𝜓→𝜑¬𝜓Modus ponens 4546, 4564
4566→↔¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into biimp
4567→→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓Subs [𝜑↗→¬¬→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into ax-1
4568→¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓Modus ponens 501, 4567
4569→→¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓→→¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓→𝜑¬𝜓Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬¬→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
4570→→¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓→𝜑¬𝜓Modus ponens 4568, 4569
4571→¬⋀𝜑𝜓→𝜑¬𝜓Modus ponens 4563, 4570
4572→→→𝜑¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓→𝜑¬𝜓↔→𝜑¬𝜓¬⋀𝜑𝜓Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into impbi
4573→→¬⋀𝜑𝜓→𝜑¬𝜓↔→𝜑¬𝜓¬⋀𝜑𝜓Modus ponens 4559, 4572
4574↔→𝜑¬𝜓¬⋀𝜑𝜓Modus ponens 4571, 4573imnan
4575→↔𝜓¬¬𝜓→𝜑↔𝜓¬¬𝜓Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1
4576→𝜑↔𝜓¬¬𝜓Modus ponens 1915, 4575
4577↔→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓Subs [𝜒↗¬¬𝜓] into pm5.74
4578→↔→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓→→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓Subs [𝜑↗→𝜑↔𝜓¬¬𝜓, 𝜓↗↔→𝜑𝜓→𝜑¬¬𝜓] into biimp
4579→→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓Modus ponens 4577, 4578
4580↔→𝜑𝜓→𝜑¬¬𝜓Modus ponens 4576, 4579
4581↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓Subs [𝜓↗¬𝜓] into imnan
4582→↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗¬⋀𝜑¬𝜓] into biimp
4583→→𝜑¬¬𝜓¬⋀𝜑¬𝜓Modus ponens 4581, 4582
4584→↔→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into biimp
4585→→𝜑𝜓→𝜑¬¬𝜓Modus ponens 4580, 4584
4586→→→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓Subs [𝜑↗→→𝜑¬¬𝜓¬⋀𝜑¬𝜓, 𝜓↗→𝜑𝜓] into ax-1
4587→→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓Modus ponens 4583, 4586
4588→→→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓¬⋀𝜑¬𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗¬⋀𝜑¬𝜓] into ax-2
4589→→→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓¬⋀𝜑¬𝜓Modus ponens 4587, 4588
4590→→𝜑𝜓¬⋀𝜑¬𝜓Modus ponens 4585, 4589
4591→↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗¬⋀𝜑¬𝜓] into bicom1
4592↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓Modus ponens 4581, 4591
4593→↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑¬¬𝜓Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑¬¬𝜓] into biimp
4594→¬⋀𝜑¬𝜓→𝜑¬¬𝜓Modus ponens 4592, 4593
4595→↔→𝜑𝜓→𝜑¬¬𝜓↔→𝜑¬¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into bicom1
4596↔→𝜑¬¬𝜓→𝜑𝜓Modus ponens 4580, 4595
4597→↔→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗→𝜑𝜓] into biimp
4598→→𝜑¬¬𝜓→𝜑𝜓Modus ponens 4596, 4597
4599→→→𝜑¬¬𝜓→𝜑𝜓→¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓Subs [𝜑↗→→𝜑¬¬𝜓→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into ax-1
4600→¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓Modus ponens 4598, 4599
4601→→¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓→→¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑𝜓Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗→𝜑𝜓] into ax-2
4602→→¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑𝜓Modus ponens 4600, 4601
4603→¬⋀𝜑¬𝜓→𝜑𝜓Modus ponens 4594, 4602
4604→→→𝜑𝜓¬⋀𝜑¬𝜓→→¬⋀𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓¬⋀𝜑¬𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into impbi
4605→→¬⋀𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓¬⋀𝜑¬𝜓Modus ponens 4590, 4604
4606↔→𝜑𝜓¬⋀𝜑¬𝜓Modus ponens 4603, 4605iman
4607↔→𝜑𝜑¬⋀𝜑¬𝜑Subs [𝜓↗𝜑] into iman
4608→↔→𝜑𝜑¬⋀𝜑¬𝜑→→𝜑𝜑¬⋀𝜑¬𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗¬⋀𝜑¬𝜑] into biimp
4609→→𝜑𝜑¬⋀𝜑¬𝜑Modus ponens 4607, 4608
4610¬⋀𝜑¬𝜑Modus ponens id, 4609pm3.24
4611↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓Subs [𝜑↗⋀𝜑¬𝜓] into notnotb
4612→↔→𝜑𝜓¬⋀𝜑¬𝜓↔¬⋀𝜑¬𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into bicom1
4613↔¬⋀𝜑¬𝜓→𝜑𝜓Modus ponens iman, 4612
4614↔↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑𝜓] into notbi
4615→↔↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓→↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓Subs [𝜑↗↔¬⋀𝜑¬𝜓→𝜑𝜓, 𝜓↗↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓] into biimp
4616→↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓Modus ponens 4614, 4615
4617↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓Modus ponens 4613, 4616
4618→↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into biimp
4619→¬¬⋀𝜑¬𝜓¬→𝜑𝜓Modus ponens 4617, 4618
4620→↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into biimp
4621→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓Modus ponens 4611, 4620
4622→→¬¬⋀𝜑¬𝜓¬→𝜑𝜓→⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓Subs [𝜑↗→¬¬⋀𝜑¬𝜓¬→𝜑𝜓, 𝜓↗⋀𝜑¬𝜓] into ax-1
4623→⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓Modus ponens 4619, 4622
4624→→⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓→→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬→𝜑𝜓Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
4625→→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬→𝜑𝜓Modus ponens 4623, 4624
4626→⋀𝜑¬𝜓¬→𝜑𝜓Modus ponens 4621, 4625
4627→↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into bicom1
4628↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓Modus ponens 4617, 4627
4629→↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓¬¬⋀𝜑¬𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into biimp
4630→¬→𝜑𝜓¬¬⋀𝜑¬𝜓Modus ponens 4628, 4629
4631→↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into bicom1
4632↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓Modus ponens 4611, 4631
4633→↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗⋀𝜑¬𝜓] into biimp
4634→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓Modus ponens 4632, 4633
4635→→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓Subs [𝜑↗→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
4636→¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓Modus ponens 4634, 4635
4637→→¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→→¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓⋀𝜑¬𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬⋀𝜑¬𝜓, 𝜒↗⋀𝜑¬𝜓] into ax-2
4638→→¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓⋀𝜑¬𝜓Modus ponens 4636, 4637
4639→¬→𝜑𝜓⋀𝜑¬𝜓Modus ponens 4630, 4638
4640→→⋀𝜑¬𝜓¬→𝜑𝜓→→¬→𝜑𝜓⋀𝜑¬𝜓↔⋀𝜑¬𝜓¬→𝜑𝜓Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into impbi
4641→→¬→𝜑𝜓⋀𝜑¬𝜓↔⋀𝜑¬𝜓¬→𝜑𝜓Modus ponens 4626, 4640
4642↔⋀𝜑¬𝜓¬→𝜑𝜓Modus ponens 4639, 4641annim
4643→↔⋀𝜑¬𝜓¬→𝜑𝜓↔¬→𝜑𝜓⋀𝜑¬𝜓Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into bicom1
4644↔¬→𝜑𝜓⋀𝜑¬𝜓Modus ponens annim, 4643pm4.61
4645↔¬→¬𝜑𝜓⋀¬𝜑¬𝜓Subs [𝜑↗¬𝜑] into pm4.61pm4.65
4646→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒] into id
4647→⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓] into id
4648→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4649→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓Subs [𝜑↗→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
4650→⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓Modus ponens 4648, 4649
4651→→⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒⋀𝜑𝜓] into ax-2
4652→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓Modus ponens 4650, 4651
4653→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-2
4654→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4646, 4653
4655→→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
4656→⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4654, 4655
4657→→⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→⋀𝜑𝜓𝜒⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2
4658→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4656, 4657
4659→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4648, 4658
4660→↔¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓] into biimp
4661→¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens pm4.63, 4660
4662→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
4663→¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4659, 4662
4664→→¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2
4665→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4663, 4664
4666→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4661, 4665
4667→→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-1
4668→𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4666, 4667
4669→→𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2
4670→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4668, 4669
4671→→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4672→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4670, 4671
4673→→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-2
4674→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4672, 4673
4675→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens pm3.2im, 4674
4676→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗𝜒] into pm2.27
4677→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒Subs [𝜑↗→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜓↗𝜑] into ax-1
4678→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒Modus ponens 4676, 4677
4679→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4680→→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜑↗→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4681→𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4679, 4680
4682→→𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒Subs [𝜓↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-2
4683→→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4681, 4682
4684→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒Modus ponens 4675, 4683
4685→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜒, 𝜒↗𝜓] into imim2
4686→→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Subs [𝜑↗→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4687→→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Modus ponens 4685, 4686
4688→→→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜒↗→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒] into ax-2
4689→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Modus ponens 4687, 4688
4690→→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
4691→𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Modus ponens 4689, 4690
4692→→𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Subs [𝜓↗→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒] into ax-2
4693→→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Modus ponens 4691, 4692
4694→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒Modus ponens 4678, 4693
4695→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→𝜓𝜒] into ax-2
4696→→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
4697→𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 4695, 4696
4698→→𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜓↗→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜒↗→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
4699→→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 4697, 4698
4700→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 4694, 4699
4701→→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
4702→→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 4700, 4701
4703→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 4684, 4702
4704→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
4705→→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4706→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒Modus ponens 4704, 4705
4707→→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→⋀𝜑𝜓𝜒] into ax-2
4708→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒Modus ponens 4706, 4707
4709→→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Subs [𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
4710→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Modus ponens 4703, 4709
4711→→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4712→→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Modus ponens 4710, 4711
4713→→→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
4714→→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Modus ponens 4712, 4713
4715→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Modus ponens 4704, 4714pm3.3
4716→𝜓→→𝜑→𝜓𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1
4717→→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→𝜓→→𝜑→𝜓𝜒𝜓Subs [𝜑↗→𝜓→→𝜑→𝜓𝜒𝜓] into ax-1
4718→𝜓→𝜓→→𝜑→𝜓𝜒𝜓Modus ponens 4716, 4717
4719→→𝜓→𝜓→→𝜑→𝜓𝜒𝜓→→𝜓𝜓→𝜓→→𝜑→𝜓𝜒𝜓Subs [𝜑↗𝜓, 𝜒↗→→𝜑→𝜓𝜒𝜓] into ax-2
4720→→𝜓𝜓→𝜓→→𝜑→𝜓𝜒𝜓Modus ponens 4718, 4719
4721→→→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
4722→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens pm2.04, 4721
4723→→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1
4724→𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 4722, 4723
4725→→𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜓, 𝜒↗→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2
4726→→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 4724, 4725
4727→𝜓→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 4716, 4726
4728→→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→𝜑𝜒𝜒Subs [𝜑↗→𝜑→→𝜑𝜒𝜒] into ax-1
4729→𝜓→𝜑→→𝜑𝜒𝜒Modus ponens 264, 4728
4730→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4731→→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1
4732→𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 4730, 4731
4733→→𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→𝜑→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2
4734→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 4732, 4733
4735→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒Modus ponens 4727, 4734
4736→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒, 𝜒↗→𝜑→𝜓𝜒] into imim2
4737→→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4738→𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Modus ponens 4736, 4737
4739→→𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-2
4740→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Modus ponens 4738, 4739
4741→→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-1
4742→𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Modus ponens 4740, 4741
4743→→𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-2
4744→→𝜓→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Modus ponens 4742, 4743
4745→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒Modus ponens 4729, 4744
4746→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒Subs [𝜓↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4747→→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒] into ax-1
4748→𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 4746, 4747
4749→→𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒, 𝜒↗→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2
4750→→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 4748, 4749
4751→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 4745, 4750
4752→→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2
4753→→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 4751, 4752
4754→𝜓→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 4735, 4753
4755→→𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4756→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4754, 4755
4757→→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒→𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4758→𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4756, 4757
4759→→𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒→→𝜑→𝜓𝜑→𝜑→𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓→→𝜑→𝜓𝜒𝜒] into ax-2
4760→→𝜑→𝜓𝜑→𝜑→𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4758, 4759
4761→𝜑→𝜓→→𝜑→𝜓𝜒𝜒Modus ponens ax-1, 4760
4762→→𝜑→𝜓→→𝜑→𝜓𝜒𝜒→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒Subs [𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4763→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 4761, 4762
4764→→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒→¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1
4765→¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 4763, 4764
4766→→¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2
4767→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 4765, 4766
4768→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒Modus ponens 575, 4767
4769→→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4770→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4768, 4769
4771→→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4772→𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4770, 4771
4773→→𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓→→𝜑→𝜓𝜒𝜒] into ax-2
4774→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4772, 4773
4775→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 581, 4774
4776→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→𝜑→𝜓𝜒𝜒] into notnot
4777→→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒→¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1
4778→¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒Modus ponens 4776, 4777
4779→→¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜒, 𝜒↗¬¬→→𝜑→𝜓𝜒𝜒] into ax-2
4780→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒Modus ponens 4778, 4779
4781→→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4782→𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒Modus ponens 4780, 4781
4783→→𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒Subs [𝜓↗→¬¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒] into ax-2
4784→→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒Modus ponens 4782, 4783
4785→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒Modus ponens 4775, 4784
4786→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-3
4787→→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓→𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓, 𝜓↗𝜑] into ax-1
4788→𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓Modus ponens 4786, 4787
4789→→𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓→→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓Subs [𝜓↗→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬𝜓] into ax-2
4790→→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓Modus ponens 4788, 4789
4791→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓Modus ponens 4785, 4790
4792→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒] into id
4793→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4794→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4795→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒Modus ponens 4793, 4794
4796→→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→𝜑¬→→𝜑→𝜓𝜒𝜒] into ax-2
4797→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒Modus ponens 4795, 4796
4798→→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓Subs [𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗¬𝜓] into ax-2
4799→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓Modus ponens 4791, 4798
4800→→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓Subs [𝜑↗→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4801→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓Modus ponens 4799, 4800
4802→→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→𝜑¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→𝜑¬𝜓] into ax-2
4803→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓Modus ponens 4801, 4802
4804→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓Modus ponens 4793, 4803
4805→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4806→¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 619, 4805
4807→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4808→→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4809→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Modus ponens 4807, 4808
4810→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓] into ax-2
4811→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Modus ponens 4809, 4810
4812→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Modus ponens 622, 4811
4813→→¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
4814→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Modus ponens 4806, 4813
4815→→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Subs [𝜑↗→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4816→¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Modus ponens 4814, 4815
4817→→¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓] into ax-2
4818→→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓Modus ponens 4816, 4817
4819→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4820→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4821→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒Modus ponens 4819, 4820
4822→→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒] into ax-2
4823→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒Modus ponens 4821, 4822
4824→→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗¬→𝜑¬𝜓] into ax-2
4825→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 4812, 4824
4826→→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4827→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 4825, 4826
4828→→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
4829→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 4827, 4828
4830→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 4819, 4829
4831→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4832→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 647, 4831
4833→→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
4834→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 4832, 4833
4835→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 4830, 4834
4836→→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
4837→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓Modus ponens 4835, 4836
4838→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓Modus ponens 4804, 4837
4839→→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-3
4840→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4838, 4839
4841→↔⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into biimp
4842→⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens df-an, 4841
4843→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒→⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜑↗→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
4844→⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4840, 4843
4845→→⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4846→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4844, 4845
4847→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒Modus ponens 4842, 4846
4848→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
4849→→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
4850→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒Modus ponens 4848, 4849
4851→→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓→𝜑→𝜓𝜒] into ax-2
4852→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒Modus ponens 4850, 4851
4853→→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-2
4854→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 4847, 4853
4855→→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
4856→→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 4854, 4855
4857→→→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
4858→→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 4856, 4857
4859→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 4848, 4858pm3.31
4860→→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into impbi
4861→→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Modus ponens pm3.3, 4860
4862↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Modus ponens pm3.31, 4861impexp
4863→⋀𝜓𝜑⋀𝜓𝜑Subs [𝜑↗⋀𝜓𝜑] into id
4864↔⋀𝜓𝜑¬→𝜓¬𝜑Subs [𝜑↗𝜓, 𝜓↗𝜑] into df-an
4865→↔⋀𝜓𝜑¬→𝜓¬𝜑↔¬→𝜓¬𝜑⋀𝜓𝜑Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into bicom1
4866↔¬→𝜓¬𝜑⋀𝜓𝜑Modus ponens 4864, 4865
4867→↔¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑] into biimp
4868→¬→𝜓¬𝜑⋀𝜓𝜑Modus ponens 4866, 4867
4869→→⋀𝜓𝜑⋀𝜓𝜑→¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑Subs [𝜑↗→⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into ax-1
4870→¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑Modus ponens 4863, 4869
4871→→¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜓𝜑] into ax-2
4872→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑Modus ponens 4870, 4871
4873→𝜓→𝜑¬→𝜓¬𝜑Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm3.2im
4874→→¬→𝜓¬𝜑⋀𝜓𝜑→𝜑→¬→𝜓¬𝜑⋀𝜓𝜑Subs [𝜑↗→¬→𝜓¬𝜑⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4875→𝜑→¬→𝜓¬𝜑⋀𝜓𝜑Modus ponens 4868, 4874
4876→→𝜑→¬→𝜓¬𝜑⋀𝜓𝜑→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑Subs [𝜓↗¬→𝜓¬𝜑, 𝜒↗⋀𝜓𝜑] into ax-2
4877→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑Modus ponens 4875, 4876
4878→→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑→𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑Subs [𝜑↗→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑] into ax-1
4879→𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑Modus ponens 4877, 4878
4880→→𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑⋀𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗→𝜑¬→𝜓¬𝜑, 𝜒↗→𝜑⋀𝜓𝜑] into ax-2
4881→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑⋀𝜓𝜑Modus ponens 4879, 4880
4882→𝜓→𝜑⋀𝜓𝜑Modus ponens 4873, 4881
4883→→𝜓→𝜑⋀𝜓𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into ax-2
4884→→𝜓𝜑→𝜓⋀𝜓𝜑Modus ponens 4882, 4883
4885→→→𝜓𝜑→𝜓⋀𝜓𝜑→𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑Subs [𝜑↗→→𝜓𝜑→𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4886→𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑Modus ponens 4884, 4885
4887→→𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑→→𝜑→𝜓𝜑→𝜑→𝜓⋀𝜓𝜑Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓⋀𝜓𝜑] into ax-2
4888→→𝜑→𝜓𝜑→𝜑→𝜓⋀𝜓𝜑Modus ponens 4886, 4887
4889→𝜑→𝜓⋀𝜓𝜑Modus ponens ax-1, 4888pm3.21
4890→→𝜑→𝜓⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜓𝜑Subs [𝜒↗⋀𝜓𝜑] into ax-2
4891→→𝜑𝜓→𝜑⋀𝜓𝜑Modus ponens pm3.21, 4890ancr
4892→→→𝜑𝜓→𝜑⋀𝜓𝜑→¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜑, 𝜓↗¬¬𝜓] into ax-1
4893→¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑Modus ponens ancr, 4892
4894→→¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑⋀𝜓𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜓𝜑] into ax-2
4895→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑⋀𝜓𝜑Modus ponens 4893, 4894
4896→¬¬𝜓→𝜑⋀𝜓𝜑Modus ponens 575, 4895
4897→→¬¬𝜓→𝜑⋀𝜓𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into ax-2
4898→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑Modus ponens 4896, 4897
4899→→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4900→𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑Modus ponens 4898, 4899
4901→→𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓⋀𝜓𝜑Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓⋀𝜓𝜑] into ax-2
4902→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓⋀𝜓𝜑Modus ponens 4900, 4901
4903→𝜑→¬¬𝜓⋀𝜓𝜑Modus ponens 581, 4902
4904→⋀𝜓𝜑¬¬⋀𝜓𝜑Subs [𝜑↗⋀𝜓𝜑] into notnot
4905→→⋀𝜓𝜑¬¬⋀𝜓𝜑→¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑Subs [𝜑↗→⋀𝜓𝜑¬¬⋀𝜓𝜑, 𝜓↗¬¬𝜓] into ax-1
4906→¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑Modus ponens 4904, 4905
4907→→¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜓𝜑, 𝜒↗¬¬⋀𝜓𝜑] into ax-2
4908→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑Modus ponens 4906, 4907
4909→→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑Subs [𝜑↗→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4910→𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑Modus ponens 4908, 4909
4911→→𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑→→𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜓𝜑Subs [𝜓↗→¬¬𝜓⋀𝜓𝜑, 𝜒↗→¬¬𝜓¬¬⋀𝜓𝜑] into ax-2
4912→→𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜓𝜑Modus ponens 4910, 4911
4913→𝜑→¬¬𝜓¬¬⋀𝜓𝜑Modus ponens 4903, 4912
4914→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-3
4915→→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓→𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓, 𝜓↗𝜑] into ax-1
4916→𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓Modus ponens 4914, 4915
4917→→𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓→→𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→¬⋀𝜓𝜑¬𝜓Subs [𝜓↗→¬¬𝜓¬¬⋀𝜓𝜑, 𝜒↗→¬⋀𝜓𝜑¬𝜓] into ax-2
4918→→𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→¬⋀𝜓𝜑¬𝜓Modus ponens 4916, 4917
4919→𝜑→¬⋀𝜓𝜑¬𝜓Modus ponens 4913, 4918
4920→¬⋀𝜓𝜑¬⋀𝜓𝜑Subs [𝜑↗¬⋀𝜓𝜑] into id
4921→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4922→→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑Subs [𝜑↗→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑] into ax-1
4923→¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑Modus ponens 4921, 4922
4924→→¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑, 𝜒↗→𝜑¬⋀𝜓𝜑] into ax-2
4925→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑Modus ponens 4923, 4924
4926→→𝜑→¬⋀𝜓𝜑¬𝜓→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓Subs [𝜓↗¬⋀𝜓𝜑, 𝜒↗¬𝜓] into ax-2
4927→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓Modus ponens 4919, 4926
4928→→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓Subs [𝜑↗→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4929→¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓Modus ponens 4927, 4928
4930→→¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓→→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬𝜓Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→𝜑¬⋀𝜓𝜑, 𝜒↗→𝜑¬𝜓] into ax-2
4931→→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬𝜓Modus ponens 4929, 4930
4932→¬⋀𝜓𝜑→𝜑¬𝜓Modus ponens 4921, 4931
4933→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4934→¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 619, 4933
4935→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4936→→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4937→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Modus ponens 4935, 4936
4938→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬⋀𝜓𝜑¬→𝜑¬𝜓] into ax-2
4939→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Modus ponens 4937, 4938
4940→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Modus ponens 622, 4939
4941→→¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
4942→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Modus ponens 4934, 4941
4943→→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Subs [𝜑↗→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4944→¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Modus ponens 4942, 4943
4945→→¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜒↗→¬⋀𝜓𝜑¬→𝜑¬𝜓] into ax-2
4946→→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓Modus ponens 4944, 4945
4947→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4948→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑Subs [𝜑↗→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑] into ax-1
4949→¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑Modus ponens 4947, 4948
4950→→¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑] into ax-2
4951→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑Modus ponens 4949, 4950
4952→→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2
4953→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 4940, 4952
4954→→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4955→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 4953, 4954
4956→→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
4957→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 4955, 4956
4958→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 4947, 4957
4959→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4960→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 647, 4959
4961→→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
4962→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 4960, 4961
4963→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 4958, 4962
4964→→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑¬¬→𝜑¬𝜓Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
4965→→¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑¬¬→𝜑¬𝜓Modus ponens 4963, 4964
4966→¬⋀𝜓𝜑¬¬→𝜑¬𝜓Modus ponens 4932, 4965
4967→→¬⋀𝜓𝜑¬¬→𝜑¬𝜓→¬→𝜑¬𝜓⋀𝜓𝜑Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜑¬𝜓] into ax-3
4968→¬→𝜑¬𝜓⋀𝜓𝜑Modus ponens 4966, 4967
4969→→¬→𝜑¬𝜓⋀𝜓𝜑→⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑Subs [𝜑↗→¬→𝜑¬𝜓⋀𝜓𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
4970→⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑Modus ponens 4968, 4969
4971→→⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜓𝜑] into ax-2
4972→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜓𝜑Modus ponens 4970, 4971
4973→⋀𝜑𝜓⋀𝜓𝜑Modus ponens 4842, 4972pm3.22
4974→⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm3.22
4975→→⋀𝜑𝜓⋀𝜓𝜑→→⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into impbi
4976→→⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑Modus ponens pm3.22, 4975
4977↔⋀𝜑𝜓⋀𝜓𝜑Modus ponens 4974, 4976ancom
4978→↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀𝜑𝜓𝜒→⋀𝜓𝜑𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into imbi1
4979↔→⋀𝜑𝜓𝜒→⋀𝜓𝜑𝜒Modus ponens ancom, 4978ancomst
4980→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒] into id
4981↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜓↗⋀𝜓𝜒] into df-an
4982→↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into bicom1
4983↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4981, 4982
4984→↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
4985→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4983, 4984
4986→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1
4987→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4980, 4986
4988→→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
4989→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4987, 4988
4990→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜓↗⋀𝜓𝜒] into pm3.2im
4991→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
4992→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4985, 4991
4993→→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
4994→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4992, 4993
4995→→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
4996→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4994, 4995
4997→→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒] into ax-2
4998→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4996, 4997
4999→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4990, 4998
5000→⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒] into id
5001→⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5002→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
5003→⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 5001, 5002
5004→→⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5005→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 5003, 5004
5006→→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
5007→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 4999, 5006
5008→→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
5009→⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5007, 5008
5010→→⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5011→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5009, 5010
5012→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5001, 5011
5013↔⋀𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into df-an
5014→↔⋀𝜓𝜒¬→𝜓¬𝜒↔¬→𝜓¬𝜒⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into bicom1
5015↔¬→𝜓¬𝜒⋀𝜓𝜒Modus ponens 5013, 5014
5016→↔¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒⋀𝜓𝜒Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒] into biimp
5017→¬→𝜓¬𝜒⋀𝜓𝜒Modus ponens 5015, 5016
5018→→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-1
5019→¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5012, 5018
5020→→¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5021→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5019, 5020
5022→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5017, 5021
5023→𝜓→𝜒¬→𝜓¬𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm3.2im
5024→→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
5025→𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5022, 5024
5026→→𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5027→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5025, 5026
5028→→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-1
5029→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5027, 5028
5030→→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5031→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5029, 5030
5032→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5023, 5031
5033→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜓↗⋀𝜑⋀𝜓𝜒] into pm2.27
5034→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5035→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5033, 5034
5036→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5037→→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-1
5038→𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5036, 5037
5039→→𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5040→→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5038, 5039
5041→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒Modus ponens 5032, 5040
5042→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into imim2
5043→→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5044→𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5042, 5043
5045→→𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜓↗→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5046→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5044, 5045
5047→→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5048→𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5046, 5047
5049→→𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5050→→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5048, 5049
5051→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5035, 5050
5052→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜓↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5053→→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5054→𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5052, 5053
5055→→𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5056→→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5054, 5055
5057→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5051, 5056
5058→→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5059→→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5057, 5058
5060→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5041, 5059
5061→→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5062→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5060, 5061
5063→→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5064→𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5062, 5063
5065→→𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜓𝜑→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5066→→𝜑→𝜓𝜑→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5064, 5065
5067→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens ax-1, 5066
5068→→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5069→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5067, 5068
5070→→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1
5071→¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5069, 5070
5072→→¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5073→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5071, 5072
5074→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 575, 5073
5075→→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5076→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5074, 5075
5077→→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5078→𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5076, 5077
5079→→𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5080→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5078, 5079
5081→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 581, 5080
5082→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→𝜒⋀𝜑⋀𝜓𝜒] into notnot
5083→→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1
5084→¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5082, 5083
5085→→¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5086→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5084, 5085
5087→→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5088→𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5086, 5087
5089→→𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜓↗→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5090→→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5088, 5089
5091→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5081, 5090
5092→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-3
5093→→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓, 𝜓↗𝜑] into ax-1
5094→𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓Modus ponens 5092, 5093
5095→→𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓Subs [𝜓↗→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓] into ax-2
5096→→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓Modus ponens 5094, 5095
5097→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓Modus ponens 5091, 5096
5098→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒] into id
5099→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5100→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5101→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5099, 5100
5102→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5103→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5101, 5102
5104→→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓Subs [𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬𝜓] into ax-2
5105→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓Modus ponens 5097, 5104
5106→→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓Subs [𝜑↗→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5107→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓Modus ponens 5105, 5106
5108→→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑¬𝜓] into ax-2
5109→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓Modus ponens 5107, 5108
5110→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓Modus ponens 5099, 5109
5111→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5112→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 619, 5111
5113→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5114→→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5115→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Modus ponens 5113, 5114
5116→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓] into ax-2
5117→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Modus ponens 5115, 5116
5118→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Modus ponens 622, 5117
5119→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
5120→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Modus ponens 5112, 5119
5121→→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Subs [𝜑↗→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5122→¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Modus ponens 5120, 5121
5123→→¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓] into ax-2
5124→→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓Modus ponens 5122, 5123
5125→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5126→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5127→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5125, 5126
5128→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5129→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5127, 5128
5130→→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬→𝜑¬𝜓] into ax-2
5131→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 5118, 5130
5132→→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5133→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 5131, 5132
5134→→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
5135→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 5133, 5134
5136→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 5125, 5135
5137→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5138→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 647, 5137
5139→→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
5140→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 5138, 5139
5141→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 5136, 5140
5142→→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
5143→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓Modus ponens 5141, 5142
5144→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓Modus ponens 5110, 5143
5145→→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-3
5146→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5144, 5145
5147→→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5148→⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5146, 5147
5149→→⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5150→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5148, 5149
5151→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒Modus ponens 4842, 5150
5152↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into df-an
5153→¬¬𝜒𝜒Subs [𝜑↗𝜒] into notnotr
5154→𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5155→→𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜒→⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5156→¬¬𝜒→𝜒→⋀𝜑𝜓𝜒Modus ponens 5154, 5155
5157→→¬¬𝜒→𝜒→⋀𝜑𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
5158→→¬¬𝜒𝜒→¬¬𝜒→⋀𝜑𝜓𝜒Modus ponens 5156, 5157
5159→¬¬𝜒→⋀𝜑𝜓𝜒Modus ponens 5153, 5158
5160→→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
5161→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒Modus ponens 5151, 5160
5162→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5163→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒Modus ponens 5161, 5162
5164→→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒] into ax-2
5165→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒Modus ponens 5163, 5164
5166→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒Modus ponens 5159, 5165
5167→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1
5168→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓Subs [𝜑↗→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
5169→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓Modus ponens 5167, 5168
5170→→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→¬¬𝜒⋀𝜑𝜓] into ax-2
5171→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓Modus ponens 5169, 5170
5172→→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
5173→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5166, 5172
5174→→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5175→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5173, 5174
5176→→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5177→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5175, 5176
5178→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5167, 5177
5179→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒] into notnot
5180→→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒→¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5181→¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒Modus ponens 5179, 5180
5182→→¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗¬¬⋀𝜑⋀𝜓𝜒] into ax-2
5183→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒Modus ponens 5181, 5182
5184→→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5185→⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒Modus ponens 5183, 5184
5186→→⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒] into ax-2
5187→→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒Modus ponens 5185, 5186
5188→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒Modus ponens 5178, 5187
5189→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-3
5190→→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5191→⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒Modus ponens 5189, 5190
5192→→⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬𝜒] into ax-2
5193→→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒Modus ponens 5191, 5192
5194→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒Modus ponens 5188, 5193
5195→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒] into id
5196→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5197→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5198→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒Modus ponens 5196, 5197
5199→→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒] into ax-2
5200→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒Modus ponens 5198, 5199
5201→→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2
5202→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Modus ponens 5194, 5201
5203→→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5204→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Modus ponens 5202, 5203
5205→→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
5206→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Modus ponens 5204, 5205
5207→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Modus ponens 5196, 5206
5208→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒] into id
5209→→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5210→¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5208, 5209
5211→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒] into notnotr
5212→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5213→→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
5214→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5212, 5213
5215→→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
5216→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5214, 5215
5217→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5211, 5216
5218→→¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
5219→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5210, 5218
5220→→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
5221→¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5219, 5220
5222→→¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
5223→→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5221, 5222
5224→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
5225→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5226→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒Modus ponens 5224, 5225
5227→→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒] into ax-2
5228→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒Modus ponens 5226, 5227
5229→→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
5230→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5217, 5229
5231→→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5232→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5230, 5231
5233→→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
5234→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5232, 5233
5235→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5224, 5234
5236→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-3
5237→→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5238→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 5236, 5237
5239→→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2
5240→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 5238, 5239
5241→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 5235, 5240
5242→→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2
5243→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 5241, 5242
5244→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 5207, 5243
5245→→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3
5246→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5244, 5245
5247→↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into biimp
5248→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5152, 5247
5249→→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
5250→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5246, 5249
5251→→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
5252→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5250, 5251
5253→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5248, 5252
5254→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒] into id
5255→↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into bicom1
5256↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5152, 5255
5257→↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
5258→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5256, 5257
5259→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-1
5260→¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5254, 5259
5261→→¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5262→→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5260, 5261
5263→⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into pm3.2im
5264→→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5265→𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5258, 5264
5266→→𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5267→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5265, 5266
5268→→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5269→⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5267, 5268
5270→→⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5271→→⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5269, 5270
5272→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5263, 5271
5273→→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒→¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
5274→¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5272, 5273
5275→→¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5276→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5274, 5275
5277→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 4661, 5276
5278→→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-1
5279→𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5277, 5278
5280→→𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5281→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5279, 5280
5282→→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5283→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5281, 5282
5284→→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5285→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5283, 5284
5286→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens pm3.2im, 5285
5287→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into pm2.27
5288→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5289→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5287, 5288
5290→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5291→→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5292→𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5290, 5291
5293→→𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒Subs [𝜓↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5294→→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5292, 5293
5295→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5286, 5294
5296→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into imim2
5297→→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5298→𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5296, 5297
5299→→𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5300→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5298, 5299
5301→→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5302→𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5300, 5301
5303→→𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜓↗→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5304→→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5302, 5303
5305→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5289, 5304
5306→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5307→→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5308→𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5306, 5307
5309→→𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜓↗→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5310→→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5308, 5309
5311→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5305, 5310
5312→→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜓↗→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5313→→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5311, 5312
5314→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5295, 5313
5315→→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜓↗𝜒, 𝜒↗→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5316→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5314, 5315
5317→→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5318→𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5316, 5317
5319→→𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜑𝜒→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5320→→𝜒→𝜑𝜒→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5318, 5319
5321→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 1834, 5320
5322→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into pm2.27
5323→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5324→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5322, 5323
5325→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-1
5326→→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5327→𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5325, 5326
5328→→𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5329→→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5327, 5328
5330→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒Modus ponens 5321, 5329
5331→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into imim2
5332→→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5333→𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5331, 5332
5334→→𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5335→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5333, 5334
5336→→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5337→𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5335, 5336
5338→→𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5339→→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5337, 5338
5340→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5324, 5339
5341→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5342→→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5343→𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5341, 5342
5344→→𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5345→→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5343, 5344
5346→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5340, 5345
5347→→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5348→→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5346, 5347
5349→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5330, 5348
5350→𝜓→𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗𝜒] into ax-1
5351→→𝜓→𝜒𝜓→𝜓→𝜓→𝜒𝜓Subs [𝜑↗→𝜓→𝜒𝜓] into ax-1
5352→𝜓→𝜓→𝜒𝜓Modus ponens 5350, 5351
5353→→𝜓→𝜓→𝜒𝜓→→𝜓𝜓→𝜓→𝜒𝜓Subs [𝜑↗𝜓, 𝜒↗→𝜒𝜓] into ax-2
5354→→𝜓𝜓→𝜓→𝜒𝜓Modus ponens 5352, 5353
5355→→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5356→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5349, 5355
5357→→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5358→𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5356, 5357
5359→→𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜒𝜓→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5360→→𝜓→𝜒𝜓→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5358, 5359
5361→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5350, 5360
5362→𝜒→𝜓𝜒Subs [𝜑↗𝜒] into ax-1
5363→→𝜒→𝜓𝜒→¬¬𝜒→𝜒→𝜓𝜒Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5364→¬¬𝜒→𝜒→𝜓𝜒Modus ponens 5362, 5363
5365→→¬¬𝜒→𝜒→𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2
5366→→¬¬𝜒𝜒→¬¬𝜒→𝜓𝜒Modus ponens 5364, 5365
5367→¬¬𝜒→𝜓𝜒Modus ponens 5153, 5366
5368→→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5369→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5361, 5368
5370→→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5371→¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5369, 5370
5372→→¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5373→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5371, 5372
5374→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5367, 5373
5375→𝜓→¬¬𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗¬¬𝜒] into ax-1
5376→→𝜓→¬¬𝜒𝜓→𝜓→𝜓→¬¬𝜒𝜓Subs [𝜑↗→𝜓→¬¬𝜒𝜓] into ax-1
5377→𝜓→𝜓→¬¬𝜒𝜓Modus ponens 5375, 5376
5378→→𝜓→𝜓→¬¬𝜒𝜓→→𝜓𝜓→𝜓→¬¬𝜒𝜓Subs [𝜑↗𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2
5379→→𝜓𝜓→𝜓→¬¬𝜒𝜓Modus ponens 5377, 5378
5380→→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5381→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5374, 5380
5382→→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5383→𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5381, 5382
5384→→𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5385→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5383, 5384
5386→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5375, 5385
5387→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→𝜑⋀⋀𝜑𝜓𝜒] into notnot
5388→→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5389→¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5387, 5388
5390→→¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5391→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5389, 5390
5392→→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5393→𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5391, 5392
5394→→𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5395→→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5393, 5394
5396→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5386, 5395
5397→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-3
5398→→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒] into ax-1
5399→𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒Modus ponens 5397, 5398
5400→→𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒] into ax-2
5401→→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒Modus ponens 5399, 5400
5402→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒Modus ponens 5396, 5401
5403→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒] into id
5404→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5405→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5406→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5404, 5405
5407→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5408→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5406, 5407
5409→→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒Subs [𝜑↗𝜓, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬𝜒] into ax-2
5410→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒Modus ponens 5402, 5409
5411→→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒Subs [𝜑↗→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5412→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒Modus ponens 5410, 5411
5413→→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓¬𝜒] into ax-2
5414→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒Modus ponens 5412, 5413
5415→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒Modus ponens 5404, 5414
5416→¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→𝜓¬𝜒] into id
5417→→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5418→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 5416, 5417
5419→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→𝜓¬𝜒] into notnotr
5420→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5421→→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
5422→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Modus ponens 5420, 5421
5423→→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒] into ax-2
5424→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Modus ponens 5422, 5423
5425→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Modus ponens 5419, 5424
5426→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
5427→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Modus ponens 5418, 5426
5428→→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
5429→¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Modus ponens 5427, 5428
5430→→¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒] into ax-2
5431→→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒Modus ponens 5429, 5430
5432→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
5433→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5434→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5432, 5433
5435→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5436→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5434, 5435
5437→→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
5438→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 5425, 5437
5439→→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5440→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 5438, 5439
5441→→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2
5442→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 5440, 5441
5443→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 5432, 5442
5444→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗¬¬→𝜓¬𝜒, 𝜓↗→𝜓¬𝜒] into ax-3
5445→→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5446→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 5444, 5445
5447→→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2
5448→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 5446, 5447
5449→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 5443, 5448
5450→→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2
5451→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒Modus ponens 5449, 5450
5452→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒Modus ponens 5415, 5451
5453→→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3
5454→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5452, 5453
5455→↔⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into biimp
5456→⋀𝜓𝜒¬→𝜓¬𝜒Modus ponens 5013, 5455
5457→→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
5458→⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5454, 5457
5459→→⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5460→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5458, 5459
5461→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5456, 5460
5462→𝜑→⋀𝜓𝜒𝜑Subs [𝜓↗⋀𝜓𝜒] into ax-1
5463→→𝜑→⋀𝜓𝜒𝜑→𝜑→𝜑→⋀𝜓𝜒𝜑Subs [𝜑↗→𝜑→⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1
5464→𝜑→𝜑→⋀𝜓𝜒𝜑Modus ponens 5462, 5463
5465→→𝜑→𝜑→⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→⋀𝜓𝜒𝜑Subs [𝜓↗𝜑, 𝜒↗→⋀𝜓𝜒𝜑] into ax-2
5466→→𝜑𝜑→𝜑→⋀𝜓𝜒𝜑Modus ponens 5464, 5465
5467→→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5468→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5461, 5467
5469→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5470→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5468, 5469
5471→→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5472→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5470, 5471
5473→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5462, 5472
5474→¬¬⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒] into notnotr
5475→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
5476→¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 5001, 5475
5477→→¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→¬¬⋀𝜓𝜒⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5478→→¬¬⋀𝜓𝜒⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 5476, 5477
5479→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 5474, 5478
5480→→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5481→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5473, 5480
5482→→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
5483→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5481, 5482
5484→→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5485→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5483, 5484
5486→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒Modus ponens 5479, 5485
5487→𝜑→¬¬⋀𝜓𝜒𝜑Subs [𝜓↗¬¬⋀𝜓𝜒] into ax-1
5488→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→𝜑→¬¬⋀𝜓𝜒𝜑Subs [𝜑↗→𝜑→¬¬⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1
5489→𝜑→𝜑→¬¬⋀𝜓𝜒𝜑Modus ponens 5487, 5488
5490→→𝜑→𝜑→¬¬⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→¬¬⋀𝜓𝜒𝜑Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜑] into ax-2
5491→→𝜑𝜑→𝜑→¬¬⋀𝜓𝜒𝜑Modus ponens 5489, 5490
5492→→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5493→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5486, 5492
5494→→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5495→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5493, 5494
5496→→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5497→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5495, 5496
5498→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5487, 5497
5499→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒] into notnot
5500→→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
5501→¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Modus ponens 5499, 5500
5502→→¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗¬¬⋀⋀𝜑𝜓𝜒] into ax-2
5503→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Modus ponens 5501, 5502
5504→→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5505→𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Modus ponens 5503, 5504
5506→→𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Subs [𝜓↗→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒] into ax-2
5507→→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Modus ponens 5505, 5506
5508→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒Modus ponens 5498, 5507
5509→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-3
5510→→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5511→𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒Modus ponens 5509, 5510
5512→→𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒] into ax-2
5513→→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒Modus ponens 5511, 5512
5514→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒Modus ponens 5508, 5513
5515→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒] into id
5516→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5517→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5518→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒Modus ponens 5516, 5517
5519→→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑¬⋀⋀𝜑𝜓𝜒] into ax-2
5520→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒Modus ponens 5518, 5519
5521→→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒Subs [𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗¬⋀𝜓𝜒] into ax-2
5522→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒Modus ponens 5514, 5521
5523→→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5524→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒Modus ponens 5522, 5523
5525→→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜑¬⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
5526→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒Modus ponens 5524, 5525
5527→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒Modus ponens 5516, 5526
5528→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒] into id
5529→→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5530→¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5528, 5529
5531→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒] into notnotr
5532→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5533→→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
5534→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5532, 5533
5535→→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
5536→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5534, 5535
5537→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5531, 5536
5538→→¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
5539→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5530, 5538
5540→→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
5541→¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5539, 5540
5542→→¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
5543→→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5541, 5542
5544→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
5545→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5546→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒Modus ponens 5544, 5545
5547→→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒] into ax-2
5548→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒Modus ponens 5546, 5547
5549→→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
5550→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5537, 5549
5551→→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5552→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5550, 5551
5553→→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
5554→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5552, 5553
5555→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5544, 5554
5556→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into ax-3
5557→→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5558→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 5556, 5557
5559→→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2
5560→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 5558, 5559
5561→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 5555, 5560
5562→→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2
5563→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 5561, 5562
5564→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 5527, 5563
5565→→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3
5566→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5564, 5565
5567→↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into biimp
5568→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 4981, 5567
5569→→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
5570→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5566, 5569
5571→→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5572→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5570, 5571
5573→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5568, 5572
5574→→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi
5575→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5253, 5574
5576↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 5573, 5575anass
5577→→⋀𝜑𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-1
5578→¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓Modus ponens 4647, 5577
5579→→¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜓] into ax-2
5580→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 5578, 5579
5581→→¬→𝜑¬𝜓⋀𝜑𝜓→𝜓→¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗→¬→𝜑¬𝜓⋀𝜑𝜓] into ax-1
5582→𝜓→¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 4661, 5581
5583→→𝜓→¬→𝜑¬𝜓⋀𝜑𝜓→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜑𝜓] into ax-2
5584→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓Modus ponens 5582, 5583
5585→→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓→𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
5586→𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓Modus ponens 5584, 5585
5587→→𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓⋀𝜑𝜓Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓⋀𝜑𝜓] into ax-2
5588→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓⋀𝜑𝜓Modus ponens 5586, 5587
5589→𝜑→𝜓⋀𝜑𝜓Modus ponens pm3.2im, 5588pm3.2
5590→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm3.2
5591→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5592→𝜑→𝜓→𝜒⋀𝜓𝜒Modus ponens 5590, 5591
5593→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Subs [𝜒↗→𝜒⋀𝜓𝜒] into ax-2
5594→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Modus ponens 5592, 5593
5595→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜓↗𝜒, 𝜒↗⋀𝜓𝜒] into ax-2
5596→→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
5597→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5595, 5596
5598→→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2
5599→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5597, 5598
5600→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5594, 5599pm3.43i
5601↔⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into df-an
5602→¬¬→𝜑𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜒] into notnotr
5603→→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
5604→→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1
5605→¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 5603, 5604
5606→→¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜑𝜒→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
5607→→¬¬→𝜑𝜒→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 5605, 5606
5608→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 5602, 5607
5609→→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5610→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens pm3.43i, 5609
5611→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1
5612→¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 5610, 5611
5613→→¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2
5614→→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 5612, 5613
5615→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 5608, 5614
5616→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜑𝜒] into ax-1
5617→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
5618→→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓Modus ponens 5616, 5617
5619→→→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜒→𝜑𝜓] into ax-2
5620→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓Modus ponens 5618, 5619
5621→→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5622→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5615, 5621
5623→→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
5624→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5622, 5623
5625→→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2
5626→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5624, 5625
5627→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5616, 5626
5628→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒] into notnot
5629→→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1
5630→¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒Modus ponens 5628, 5629
5631→→¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗¬¬→𝜑⋀𝜓𝜒] into ax-2
5632→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒Modus ponens 5630, 5631
5633→→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒Subs [𝜑↗→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
5634→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒Modus ponens 5632, 5633
5635→→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜒↗→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒] into ax-2
5636→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒Modus ponens 5634, 5635
5637→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒Modus ponens 5627, 5636
5638→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-3
5639→→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒Subs [𝜑↗→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
5640→→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒Modus ponens 5638, 5639
5641→→→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒] into ax-2
5642→→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒Modus ponens 5640, 5641
5643→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒Modus ponens 5637, 5642
5644→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒] into id
5645→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
5646→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒Subs [𝜑↗→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5647→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒Modus ponens 5645, 5646
5648→→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓¬→𝜑⋀𝜓𝜒] into ax-2
5649→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒Modus ponens 5647, 5648
5650→→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗¬→𝜑𝜒] into ax-2
5651→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒Modus ponens 5643, 5650
5652→→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5653→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒Modus ponens 5651, 5652
5654→→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓¬→𝜑𝜒] into ax-2
5655→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒Modus ponens 5653, 5654
5656→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒Modus ponens 5645, 5655
5657→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒] into id
5658→→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5659→¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5657, 5658
5660→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒] into notnotr
5661→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5662→→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1
5663→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5661, 5662
5664→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5665→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5663, 5664
5666→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5660, 5665
5667→→¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5668→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5659, 5667
5669→→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1
5670→¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5668, 5669
5671→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5672→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5670, 5671
5673→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1
5674→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒Subs [𝜑↗→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5675→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒Modus ponens 5673, 5674
5676→→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒] into ax-2
5677→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒Modus ponens 5675, 5676
5678→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5679→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5666, 5678
5680→→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5681→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5679, 5680
5682→→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5683→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5681, 5682
5684→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5673, 5683
5685→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒] into ax-3
5686→→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5687→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5685, 5686
5688→→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5689→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5687, 5688
5690→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5684, 5689
5691→→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒, 𝜒↗¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5692→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5690, 5691
5693→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5656, 5692
5694→→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-3
5695→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5693, 5694
5696→↔⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒] into biimp
5697→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒Modus ponens 5601, 5696
5698→→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒→⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into ax-1
5699→⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5695, 5698
5700→→⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5701→→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5699, 5700
5702→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5697, 5701pm3.43
5703↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into df-an
5704→↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into bicom1
5705↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑Modus ponens 5703, 5704
5706→↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into biimp
5707→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑Modus ponens 5705, 5706
5708→→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
5709→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑Modus ponens 5707, 5708
5710→→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗⋀→𝜑𝜓→𝜓𝜑] into ax-2
5711→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑Modus ponens 5709, 5710
5712→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑Modus ponens 1605, 5711
5713→↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into bicom1
5714→↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into biimp
5715→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑Modus ponens 5703, 5714
5716→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into bicom1
5717↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens dfbi1, 5716
5718→↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗↔𝜑𝜓] into biimp
5719→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into ax-1
5720→⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓Modus ponens 1371, 5719
5721→→⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
5722→→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens 5720, 5721
5723→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens 5715, 5722
5724→→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into impbi
5725→→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑Modus ponens 5712, 5724
5726↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑Modus ponens 5723, 5725dfbi2
5727↔↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into dfbi2
5728→↔↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑, 𝜓↗⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓] into biimp
5729→↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens 5727, 5728
5730⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens dfbi2, 5729dfbi
5731→→𝜑→𝜓𝜑→→𝜑𝜓→𝜑𝜑Subs [𝜒↗𝜑] into ax-2
5732→→→𝜑𝜓→𝜑𝜑→¬¬𝜓→→𝜑𝜓→𝜑𝜑Subs [𝜑↗→→𝜑𝜓→𝜑𝜑, 𝜓↗¬¬𝜓] into ax-1
5733→¬¬𝜓→→𝜑𝜓→𝜑𝜑Modus ponens 1148, 5732
5734→→¬¬𝜓→→𝜑𝜓→𝜑𝜑→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜑] into ax-2
5735→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜑Modus ponens 5733, 5734
5736→¬¬𝜓→𝜑𝜑Modus ponens 575, 5735
5737→→¬¬𝜓→𝜑𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2
5738→→¬¬𝜓𝜑→¬¬𝜓𝜑Modus ponens 5736, 5737
5739→→→¬¬𝜓𝜑→¬¬𝜓𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓𝜑, 𝜓↗𝜑] into ax-1
5740→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑Modus ponens 5738, 5739
5741→→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜑Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓𝜑] into ax-2
5742→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜑Modus ponens 5740, 5741
5743→→𝜑¬¬𝜑→¬¬𝜓→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜓] into ax-1
5744→¬¬𝜓→𝜑¬¬𝜑Modus ponens notnot, 5743
5745→→¬¬𝜓→𝜑¬¬𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
5746→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑Modus ponens 5744, 5745
5747→→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑, 𝜓↗𝜑] into ax-1
5748→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑Modus ponens 5746, 5747
5749→→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬𝜑Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2
5750→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬𝜑Modus ponens 5748, 5749
5751→𝜑→¬¬𝜓¬¬𝜑Modus ponens 581, 5750
5752→→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓, 𝜓↗𝜑] into ax-1
5753→𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓Modus ponens 2033, 5752
5754→→𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→→𝜑→¬¬𝜓¬¬𝜑→𝜑→¬𝜑¬𝜓Subs [𝜓↗→¬¬𝜓¬¬𝜑, 𝜒↗→¬𝜑¬𝜓] into ax-2
5755→→𝜑→¬¬𝜓¬¬𝜑→𝜑→¬𝜑¬𝜓Modus ponens 5753, 5754
5756→𝜑→¬𝜑¬𝜓Modus ponens 5751, 5755
5757→→¬𝜑→𝜑¬𝜑→¬𝜑→¬𝜑→𝜑¬𝜑Subs [𝜑↗→¬𝜑→𝜑¬𝜑, 𝜓↗¬𝜑] into ax-1
5758→¬𝜑→¬𝜑→𝜑¬𝜑Modus ponens 414, 5757
5759→→¬𝜑→¬𝜑→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑→𝜑¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2
5760→→¬𝜑¬𝜑→¬𝜑→𝜑¬𝜑Modus ponens 5758, 5759
5761→→𝜑→¬𝜑¬𝜓→→𝜑¬𝜑→𝜑¬𝜓Subs [𝜓↗¬𝜑, 𝜒↗¬𝜓] into ax-2
5762→→𝜑¬𝜑→𝜑¬𝜓Modus ponens 5756, 5761
5763→→→𝜑¬𝜑→𝜑¬𝜓→¬𝜑→→𝜑¬𝜑→𝜑¬𝜓Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5764→¬𝜑→→𝜑¬𝜑→𝜑¬𝜓Modus ponens 5762, 5763
5765→→¬𝜑→→𝜑¬𝜑→𝜑¬𝜓→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜓] into ax-2
5766→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜓Modus ponens 5764, 5765
5767→¬𝜑→𝜑¬𝜓Modus ponens 414, 5766
5768→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5769→¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 619, 5768
5770→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5771→→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5772→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Modus ponens 5770, 5771
5773→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬𝜑¬→𝜑¬𝜓] into ax-2
5774→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Modus ponens 5772, 5773
5775→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Modus ponens 622, 5774
5776→→¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
5777→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Modus ponens 5769, 5776
5778→→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Subs [𝜑↗→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5779→¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Modus ponens 5777, 5778
5780→→¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬𝜑¬→𝜑¬𝜓, 𝜒↗→¬𝜑¬→𝜑¬𝜓] into ax-2
5781→→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓Modus ponens 5779, 5780
5782→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5783→→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
5784→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑Modus ponens 5782, 5783
5785→→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬𝜑] into ax-2
5786→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑Modus ponens 5784, 5785
5787→→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2
5788→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 5775, 5787
5789→→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5790→¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 5788, 5789
5791→→¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
5792→→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 5790, 5791
5793→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 5782, 5792
5794→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5795→¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 647, 5794
5796→→¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
5797→→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 5795, 5796
5798→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 5793, 5797
5799→→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜑→𝜑¬𝜓→¬𝜑¬¬→𝜑¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
5800→→¬𝜑→𝜑¬𝜓→¬𝜑¬¬→𝜑¬𝜓Modus ponens 5798, 5799
5801→¬𝜑¬¬→𝜑¬𝜓Modus ponens 5767, 5800
5802→→¬𝜑¬¬→𝜑¬𝜓→¬→𝜑¬𝜓𝜑Subs [𝜓↗¬→𝜑¬𝜓] into ax-3
5803→→¬→𝜑¬𝜓𝜑→⋀𝜑𝜓→¬→𝜑¬𝜓𝜑Subs [𝜑↗→¬→𝜑¬𝜓𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
5804→⋀𝜑𝜓→¬→𝜑¬𝜓𝜑Modus ponens 866, 5803
5805→→⋀𝜑𝜓→¬→𝜑¬𝜓𝜑→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜑] into ax-2
5806→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜑Modus ponens 5804, 5805
5807→⋀𝜑𝜓𝜑Modus ponens 4842, 5806simpl
5808→→𝜓→𝜑𝜓→𝜓→𝜓→𝜑𝜓Subs [𝜑↗→𝜓→𝜑𝜓] into ax-1
5809→𝜓→𝜓→𝜑𝜓Modus ponens 208, 5808
5810→→𝜓→𝜓→𝜑𝜓→→𝜓𝜓→𝜓→𝜑𝜓Subs [𝜑↗𝜓, 𝜒↗→𝜑𝜓] into ax-2
5811→→𝜓𝜓→𝜓→𝜑𝜓Modus ponens 5809, 5810
5812→→𝜑→𝜓𝜑→¬¬𝜑→𝜑→𝜓𝜑Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1
5813→¬¬𝜑→𝜑→𝜓𝜑Modus ponens ax-1, 5812
5814→→¬¬𝜑→𝜑→𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→𝜓𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→𝜓𝜑] into ax-2
5815→→¬¬𝜑𝜑→¬¬𝜑→𝜓𝜑Modus ponens 5813, 5814
5816→¬¬𝜑→𝜓𝜑Modus ponens notnotr, 5815
5817→→𝜓→𝜑𝜓→→𝜓𝜑→𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
5818→→𝜓𝜑→𝜓𝜓Modus ponens 208, 5817
5819→→→𝜓𝜑→𝜓𝜓→¬¬𝜑→→𝜓𝜑→𝜓𝜓Subs [𝜑↗→→𝜓𝜑→𝜓𝜓, 𝜓↗¬¬𝜑] into ax-1
5820→¬¬𝜑→→𝜓𝜑→𝜓𝜓Modus ponens 5818, 5819
5821→→¬¬𝜑→→𝜓𝜑→𝜓𝜓→→¬¬𝜑→𝜓𝜑→¬¬𝜑→𝜓𝜓Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜓] into ax-2
5822→→¬¬𝜑→𝜓𝜑→¬¬𝜑→𝜓𝜓Modus ponens 5820, 5821
5823→¬¬𝜑→𝜓𝜓Modus ponens 5816, 5822
5824→𝜓→¬¬𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗¬¬𝜑] into ax-1
5825→→𝜓→¬¬𝜑𝜓→𝜓→𝜓→¬¬𝜑𝜓Subs [𝜑↗→𝜓→¬¬𝜑𝜓] into ax-1
5826→𝜓→𝜓→¬¬𝜑𝜓Modus ponens 5824, 5825
5827→→𝜓→𝜓→¬¬𝜑𝜓→→𝜓𝜓→𝜓→¬¬𝜑𝜓Subs [𝜑↗𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2
5828→→𝜓𝜓→𝜓→¬¬𝜑𝜓Modus ponens 5826, 5827
5829→→¬¬𝜑→𝜓𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓Subs [𝜑↗¬¬𝜑, 𝜒↗𝜓] into ax-2
5830→→¬¬𝜑𝜓→¬¬𝜑𝜓Modus ponens 5823, 5829
5831→→→¬¬𝜑𝜓→¬¬𝜑𝜓→𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑𝜓] into ax-1
5832→𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓Modus ponens 5830, 5831
5833→→𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2
5834→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑𝜓Modus ponens 5832, 5833
5835→→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓] into ax-1
5836→𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓Modus ponens 488, 5835
5837→→𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2
5838→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑¬¬𝜓Modus ponens 5836, 5837
5839→𝜓→¬¬𝜑¬¬𝜓Modus ponens 5824, 5838
5840→→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑] into ax-1
5841→𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Modus ponens 494, 5840
5842→→𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→𝜓→¬¬𝜑¬¬𝜓→𝜓→¬𝜓¬𝜑Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
5843→→𝜓→¬¬𝜑¬¬𝜓→𝜓→¬𝜓¬𝜑Modus ponens 5841, 5842
5844→𝜓→¬𝜓¬𝜑Modus ponens 5839, 5843
5845→¬𝜓→𝜓¬𝜓Subs [𝜑↗¬𝜓] into ax-1
5846→→¬𝜓→𝜓¬𝜓→¬𝜓→¬𝜓→𝜓¬𝜓Subs [𝜑↗→¬𝜓→𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
5847→¬𝜓→¬𝜓→𝜓¬𝜓Modus ponens 5845, 5846
5848→→¬𝜓→¬𝜓→𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜓¬𝜓] into ax-2
5849→→¬𝜓¬𝜓→¬𝜓→𝜓¬𝜓Modus ponens 5847, 5848
5850→→𝜓→¬𝜓¬𝜑→→𝜓¬𝜓→𝜓¬𝜑Subs [𝜑↗𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2
5851→→𝜓¬𝜓→𝜓¬𝜑Modus ponens 5844, 5850
5852→→→𝜓¬𝜓→𝜓¬𝜑→¬𝜓→→𝜓¬𝜓→𝜓¬𝜑Subs [𝜑↗→→𝜓¬𝜓→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5853→¬𝜓→→𝜓¬𝜓→𝜓¬𝜑Modus ponens 5851, 5852
5854→→¬𝜓→→𝜓¬𝜓→𝜓¬𝜑→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜓, 𝜒↗→𝜓¬𝜑] into ax-2
5855→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜑Modus ponens 5853, 5854
5856→¬𝜓→𝜓¬𝜑Modus ponens 5845, 5855
5857→¬→𝜓¬𝜑¬→𝜓¬𝜑Subs [𝜑↗¬→𝜓¬𝜑] into id
5858→→¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑Subs [𝜑↗→¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5859→¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑Modus ponens 5857, 5858
5860→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑Subs [𝜑↗¬→𝜓¬𝜑] into notnotr
5861→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5862→→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Subs [𝜑↗→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1
5863→¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Modus ponens 5861, 5862
5864→→¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗¬→𝜓¬𝜑, 𝜒↗→¬𝜓¬→𝜓¬𝜑] into ax-2
5865→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Modus ponens 5863, 5864
5866→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Modus ponens 5860, 5865
5867→→¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜓¬𝜑, 𝜒↗¬→𝜓¬𝜑] into ax-2
5868→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Modus ponens 5859, 5867
5869→→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Subs [𝜑↗→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1
5870→¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Modus ponens 5868, 5869
5871→→¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗→¬𝜓¬→𝜓¬𝜑, 𝜒↗→¬𝜓¬→𝜓¬𝜑] into ax-2
5872→→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑Modus ponens 5870, 5871
5873→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1
5874→→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
5875→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓Modus ponens 5873, 5874
5876→→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜑¬𝜓] into ax-2
5877→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓Modus ponens 5875, 5876
5878→→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗¬𝜓, 𝜒↗¬→𝜓¬𝜑] into ax-2
5879→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑Modus ponens 5866, 5878
5880→→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑Subs [𝜑↗→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5881→¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑Modus ponens 5879, 5880
5882→→¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜑¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑] into ax-2
5883→→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑Modus ponens 5881, 5882
5884→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑Modus ponens 5873, 5883
5885→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑Subs [𝜑↗¬¬→𝜓¬𝜑, 𝜓↗→𝜓¬𝜑] into ax-3
5886→→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑→¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑Subs [𝜑↗→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5887→¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑Modus ponens 5885, 5886
5888→→¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑→→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜒↗→→𝜓¬𝜑¬¬→𝜓¬𝜑] into ax-2
5889→→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑Modus ponens 5887, 5888
5890→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑Modus ponens 5884, 5889
5891→→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑→→¬𝜓→𝜓¬𝜑→¬𝜓¬¬→𝜓¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜑, 𝜒↗¬¬→𝜓¬𝜑] into ax-2
5892→→¬𝜓→𝜓¬𝜑→¬𝜓¬¬→𝜓¬𝜑Modus ponens 5890, 5891
5893→¬𝜓¬¬→𝜓¬𝜑Modus ponens 5856, 5892
5894→→¬𝜓¬¬→𝜓¬𝜑→¬→𝜓¬𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜓¬𝜑] into ax-3
5895→¬→𝜓¬𝜑𝜓Modus ponens 5893, 5894
5896→↔⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑¬→𝜓¬𝜑Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into biimp
5897→⋀𝜓𝜑¬→𝜓¬𝜑Modus ponens 4864, 5896
5898→→¬→𝜓¬𝜑𝜓→⋀𝜓𝜑→¬→𝜓¬𝜑𝜓Subs [𝜑↗→¬→𝜓¬𝜑𝜓, 𝜓↗⋀𝜓𝜑] into ax-1
5899→⋀𝜓𝜑→¬→𝜓¬𝜑𝜓Modus ponens 5895, 5898
5900→→⋀𝜓𝜑→¬→𝜓¬𝜑𝜓→→⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑𝜓Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑, 𝜒↗𝜓] into ax-2
5901→→⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑𝜓Modus ponens 5899, 5900
5902→⋀𝜓𝜑𝜓Modus ponens 5897, 5901
5903→→⋀𝜓𝜑𝜓→¬→𝜓¬𝜑→⋀𝜓𝜑𝜓Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗¬→𝜓¬𝜑] into ax-1
5904→¬→𝜓¬𝜑→⋀𝜓𝜑𝜓Modus ponens 5902, 5903
5905→→¬→𝜓¬𝜑→⋀𝜓𝜑𝜓→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑𝜓Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗𝜓] into ax-2
5906→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑𝜓Modus ponens 5904, 5905
5907→→¬→𝜓¬𝜑𝜓→𝜑→¬→𝜓¬𝜑𝜓Subs [𝜑↗→¬→𝜓¬𝜑𝜓, 𝜓↗𝜑] into ax-1
5908→𝜑→¬→𝜓¬𝜑𝜓Modus ponens 5895, 5907
5909→→𝜑→¬→𝜓¬𝜑𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓Subs [𝜓↗¬→𝜓¬𝜑, 𝜒↗𝜓] into ax-2
5910→→𝜑¬→𝜓¬𝜑→𝜑𝜓Modus ponens 5908, 5909
5911→→→𝜑¬→𝜓¬𝜑→𝜑𝜓→𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓Subs [𝜑↗→→𝜑¬→𝜓¬𝜑→𝜑𝜓] into ax-1
5912→𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓Modus ponens 5910, 5911
5913→→𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑¬→𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2
5914→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑𝜓Modus ponens 5912, 5913
5915→→→𝜓𝜑→𝜓𝜓→𝜑→→𝜓𝜑→𝜓𝜓Subs [𝜑↗→→𝜓𝜑→𝜓𝜓, 𝜓↗𝜑] into ax-1
5916→𝜑→→𝜓𝜑→𝜓𝜓Modus ponens 5818, 5915
5917→→𝜑→→𝜓𝜑→𝜓𝜓→→𝜑→𝜓𝜑→𝜑→𝜓𝜓Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜓] into ax-2
5918→→𝜑→𝜓𝜑→𝜑→𝜓𝜓Modus ponens 5916, 5917
5919→→¬→𝜑¬𝜓𝜓→⋀𝜑𝜓→¬→𝜑¬𝜓𝜓Subs [𝜑↗→¬→𝜑¬𝜓𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
5920→⋀𝜑𝜓→¬→𝜑¬𝜓𝜓Modus ponens simprim, 5919
5921→→⋀𝜑𝜓→¬→𝜑¬𝜓𝜓→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜓] into ax-2
5922→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜓Modus ponens 5920, 5921
5923→⋀𝜑𝜓𝜓Modus ponens 4842, 5922simpr
5924→→𝜑𝜒→𝜑𝜒Modus ponens 815, 2228
5925→𝜑→→𝜑𝜒𝜑Subs [𝜓↗→𝜑𝜒] into ax-1
5926→→𝜑→→𝜑𝜒𝜑→⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑Subs [𝜑↗→𝜑→→𝜑𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
5927→⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑Modus ponens 5925, 5926
5928→→⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→→𝜑𝜒𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑𝜒𝜑] into ax-2
5929→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→→𝜑𝜒𝜑Modus ponens 5927, 5928
5930→⋀𝜑𝜓→→𝜑𝜒𝜑Modus ponens simpl, 5929
5931→→→𝜑𝜒→𝜑𝜒→→→𝜑𝜒𝜑→→𝜑𝜒𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜑] into ax-2
5932→→→𝜑𝜒𝜑→→𝜑𝜒𝜒Modus ponens 5924, 5931
5933→→→→𝜑𝜒𝜑→→𝜑𝜒𝜒→⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒Subs [𝜑↗→→→𝜑𝜒𝜑→→𝜑𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5934→⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒Modus ponens 5932, 5933
5935→→⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒→→⋀𝜑𝜓→→𝜑𝜒𝜑→⋀𝜑𝜓→→𝜑𝜒𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→𝜑𝜒𝜑, 𝜒↗→→𝜑𝜒𝜒] into ax-2
5936→→⋀𝜑𝜓→→𝜑𝜒𝜑→⋀𝜑𝜓→→𝜑𝜒𝜒Modus ponens 5934, 5935
5937→⋀𝜑𝜓→→𝜑𝜒𝜒Modus ponens 5930, 5936
5938→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5939→→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜒] into ax-1
5940→→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒Modus ponens 5938, 5939
5941→→→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→⋀𝜑𝜓→𝜑𝜒] into ax-2
5942→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒Modus ponens 5940, 5941
5943→→⋀𝜑𝜓→→𝜑𝜒𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑𝜒] into ax-2
5944→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒Modus ponens 5937, 5943
5945→→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒→→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑𝜒] into ax-1
5946→→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒Modus ponens 5944, 5945
5947→→→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒→→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗→⋀𝜑𝜓→𝜑𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
5948→→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓𝜒Modus ponens 5946, 5947
5949→→𝜑𝜒→⋀𝜑𝜓𝜒Modus ponens 5938, 5948pm3.41
5950→𝜓→𝜒𝜒Modus ponens 209, 51
5951→𝜓→→𝜓𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜓𝜒] into ax-1
5952→→𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓Subs [𝜑↗→𝜓→→𝜓𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
5953→⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓Modus ponens 5951, 5952
5954→→⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→→𝜓𝜒𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→→𝜓𝜒𝜓] into ax-2
5955→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→→𝜓𝜒𝜓Modus ponens 5953, 5954
5956→⋀𝜑𝜓→→𝜓𝜒𝜓Modus ponens simpr, 5955
5957→→→𝜓𝜒→𝜓𝜒→→→𝜓𝜒𝜓→→𝜓𝜒𝜒Subs [𝜑↗→𝜓𝜒] into ax-2
5958→→→𝜓𝜒𝜓→→𝜓𝜒𝜒Modus ponens 867, 5957
5959→→→→𝜓𝜒𝜓→→𝜓𝜒𝜒→⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒Subs [𝜑↗→→→𝜓𝜒𝜓→→𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5960→⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒Modus ponens 5958, 5959
5961→→⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒→→⋀𝜑𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→→𝜓𝜒𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→𝜓𝜒𝜓, 𝜒↗→→𝜓𝜒𝜒] into ax-2
5962→→⋀𝜑𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→→𝜓𝜒𝜒Modus ponens 5960, 5961
5963→⋀𝜑𝜓→→𝜓𝜒𝜒Modus ponens 5956, 5962
5964→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5965→→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1
5966→→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒Modus ponens 5964, 5965
5967→→→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→⋀𝜑𝜓→𝜓𝜒] into ax-2
5968→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒Modus ponens 5966, 5967
5969→→⋀𝜑𝜓→→𝜓𝜒𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-2
5970→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 5963, 5969
5971→→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1
5972→→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 5970, 5971
5973→→→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
5974→→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 5972, 5973
5975→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 5964, 5974pm3.42
5976→↔𝜑⋀𝜓𝜒→⋀𝜓𝜒𝜑Subs [𝜓↗⋀𝜓𝜒] into biimpr
5977→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
5978→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
5979→⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒Modus ponens 5977, 5978
5980→→⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒⋀𝜓𝜒] into ax-2
5981→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒Modus ponens 5979, 5980
5982→→↔𝜑⋀𝜓𝜒→⋀𝜓𝜒𝜑→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜑] into ax-2
5983→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5976, 5982
5984→→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗⋀𝜓𝜒] into ax-1
5985→⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5983, 5984
5986→→⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→↔𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2
5987→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5985, 5986
5988→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5977, 5987
5989→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗¬→𝜓¬𝜒] into ax-1
5990→¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5988, 5989
5991→→¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2
5992→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5990, 5991
5993→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5017, 5992
5994→→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜒] into ax-1
5995→𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5993, 5994
5996→→𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2
5997→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5995, 5996
5998→→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-1
5999→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5997, 5998
6000→→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-2
6001→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5999, 6000
6002→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 5023, 6001
6003→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗𝜑] into pm2.27
6004→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑] into ax-1
6005→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑Modus ponens 6003, 6004
6006→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6007→→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-1
6008→𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 6006, 6007
6009→→𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Subs [𝜑↗𝜓, 𝜓↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-2
6010→→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 6008, 6009
6011→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑Modus ponens 6002, 6010
6012→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜑] into imim2
6013→→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Subs [𝜑↗→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6014→↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Modus ponens 6012, 6013
6015→→↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→→↔𝜑⋀𝜓𝜒𝜑𝜑, 𝜒↗→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-2
6016→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Modus ponens 6014, 6015
6017→→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Subs [𝜑↗→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-1
6018→𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Modus ponens 6016, 6017
6019→→𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-2
6020→→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Modus ponens 6018, 6019
6021→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑Modus ponens 6005, 6020
6022→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→𝜒𝜑] into ax-2
6023→→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑Subs [𝜑↗→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-1
6024→𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑Modus ponens 6022, 6023
6025→→𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑, 𝜒↗→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-2
6026→→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑Modus ponens 6024, 6025
6027→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑Modus ponens 6021, 6026
6028→→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-2
6029→→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑Modus ponens 6027, 6028
6030→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑Modus ponens 6011, 6029
6031→↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔𝜑⋀𝜓𝜒] into id
6032→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒Subs [𝜑↗↔𝜑⋀𝜓𝜒] into ax-1
6033→→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6034→↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒Modus ponens 6032, 6033
6035→→↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑⋀𝜓𝜒] into ax-2
6036→→↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒Modus ponens 6034, 6035
6037→→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑Subs [𝜑↗𝜓, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜒𝜑] into ax-2
6038→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑Modus ponens 6030, 6037
6039→→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑Subs [𝜑↗→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6040→↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑Modus ponens 6038, 6039
6041→→↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜓↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓→𝜒𝜑] into ax-2
6042→→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑Modus ponens 6040, 6041
6043→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑Modus ponens 6032, 6042
6044→𝜒→→𝜒𝜑𝜑Subs [𝜑↗𝜒, 𝜓↗𝜑] into pm2.27
6045→→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑Subs [𝜑↗→𝜒→→𝜒𝜑𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6046→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑Modus ponens 6044, 6045
6047→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑Subs [𝜑↗→𝜓→𝜒𝜑, 𝜓↗𝜒] into ax-1
6048→→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑Subs [𝜑↗→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6049→↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑Modus ponens 6047, 6048
6050→→↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜓→𝜒𝜑, 𝜒↗→𝜒→𝜓→𝜒𝜑] into ax-2
6051→→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑Modus ponens 6049, 6050
6052→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑Modus ponens 6043, 6051
6053→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑Subs [𝜑↗→𝜒𝜑, 𝜓↗𝜑, 𝜒↗𝜓] into imim2
6054→→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑→𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑Subs [𝜑↗→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑, 𝜓↗𝜒] into ax-1
6055→𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑Modus ponens 6053, 6054
6056→→𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑Subs [𝜑↗𝜒, 𝜓↗→→𝜒𝜑𝜑, 𝜒↗→→𝜓→𝜒𝜑→𝜓𝜑] into ax-2
6057→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑Modus ponens 6055, 6056
6058→→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑Subs [𝜑↗→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6059→↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑Modus ponens 6057, 6058
6060→→↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→→𝜒𝜑𝜑, 𝜒↗→𝜒→→𝜓→𝜒𝜑→𝜓𝜑] into ax-2
6061→→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑Modus ponens 6059, 6060
6062→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑Modus ponens 6046, 6061
6063→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒𝜑, 𝜒↗→𝜓𝜑] into ax-2
6064→→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑Subs [𝜑↗→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6065→↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑Modus ponens 6063, 6064
6066→→↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→→𝜓→𝜒𝜑→𝜓𝜑, 𝜒↗→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑] into ax-2
6067→→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑Modus ponens 6065, 6066
6068→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑Modus ponens 6062, 6067
6069→→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→𝜓→𝜒𝜑, 𝜒↗→𝜒→𝜓𝜑] into ax-2
6070→→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑Modus ponens 6068, 6069
6071→↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑Modus ponens 6052, 6070simplbi2comt
6072→⋀𝜓𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗𝜒] into simpl
6073→→⋀𝜓𝜒𝜓→𝜑→⋀𝜓𝜒𝜓Subs [𝜑↗→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
6074→𝜑→⋀𝜓𝜒𝜓Modus ponens 6072, 6073
6075→→𝜑→⋀𝜓𝜒𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
6076→→𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 6074, 6075
6077→⋀𝜓𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into simpr
6078→→⋀𝜓𝜒𝜒→𝜑→⋀𝜓𝜒𝜒Subs [𝜑↗→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
6079→𝜑→⋀𝜓𝜒𝜒Modus ponens 6077, 6078
6080→→𝜑→⋀𝜓𝜒𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒Subs [𝜓↗⋀𝜓𝜒] into ax-2
6081→→𝜑⋀𝜓𝜒→𝜑𝜒Modus ponens 6079, 6080
6082→→𝜑𝜓→→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into pm3.2
6083→→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1
6084→→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 5603, 6083
6085→→→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
6086→→→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 6084, 6085
6087→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 6081, 6086
6088→→→𝜑𝜓→→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2
6089→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Modus ponens 6082, 6088
6090→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1
6091→→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Modus ponens 6089, 6090
6092→→→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into ax-2
6093→→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Modus ponens 6091, 6092
6094→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Modus ponens 6087, 6093
6095→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1
6096→→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
6097→→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 6095, 6096
6098→→→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒→𝜑𝜓] into ax-2
6099→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 6097, 6098
6100→→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2
6101→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6094, 6100
6102→→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
6103→→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6101, 6102
6104→→→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒] into ax-2
6105→→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6103, 6104
6106→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6095, 6105
6107→→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1
6108→→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6106, 6107
6109→→→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒] into ax-2
6110→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6108, 6109
6111→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6076, 6110
6112→→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒] into id
6113→→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2
6114→→→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6111, 6113
6115→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6112, 6114
6116→→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into impbi
6117→→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens 6115, 6116
6118↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒Modus ponens pm3.43, 6117jcab
6119→↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into bicom1
6120↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens jcab, 6119pm4.76
6121→→⋀𝜓𝜑𝜓→𝜑→⋀𝜓𝜑𝜓Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗𝜑] into ax-1
6122→𝜑→⋀𝜓𝜑𝜓Modus ponens 5902, 6121
6123→→𝜓⋀𝜓𝜑→→⋀𝜓𝜑𝜓↔𝜓⋀𝜓𝜑Subs [𝜑↗𝜓, 𝜓↗⋀𝜓𝜑] into impbi
6124→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1
6125→→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓Subs [𝜑↗→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓, 𝜓↗𝜑] into ax-1
6126→𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓Modus ponens 6124, 6125
6127→→𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓Subs [𝜓↗→⋀𝜓𝜑𝜓, 𝜒↗→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓] into ax-2
6128→→𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓Modus ponens 6126, 6127
6129→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓Modus ponens 6122, 6128
6130→→→𝜓⋀𝜓𝜑→→⋀𝜓𝜑𝜓↔𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→⋀𝜓𝜑𝜓, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2
6131→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑Modus ponens 6123, 6130
6132→→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑Subs [𝜑↗→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
6133→𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑Modus ponens 6131, 6132
6134→→𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑Subs [𝜓↗→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓, 𝜒↗→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑] into ax-2
6135→→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑Modus ponens 6133, 6134
6136→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑Modus ponens 6129, 6135
6137→→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑Subs [𝜑↗→𝜓⋀𝜓𝜑] into id
6138→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
6139→→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑Subs [𝜑↗→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1
6140→→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑Modus ponens 6138, 6139
6141→→→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗→𝜑→𝜓⋀𝜓𝜑] into ax-2
6142→→→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑Modus ponens 6140, 6141
6143→→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Subs [𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2
6144→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6136, 6143
6145→→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Subs [𝜑↗→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1
6146→→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6144, 6145
6147→→→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→𝜑→𝜓⋀𝜓𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2
6148→→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6146, 6147
6149→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6138, 6148
6150→→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Subs [𝜑↗→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
6151→𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6149, 6150
6152→→𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑Subs [𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2
6153→→𝜑→𝜓⋀𝜓𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6151, 6152
6154→𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens pm3.21, 6153
6155→→𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑Subs [𝜓↗𝜑, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2
6156→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6154, 6155
6157→→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑→𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑Subs [𝜑↗→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
6158→𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6156, 6157
6159→→𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2
6160→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑Modus ponens 6158, 6159
6161→𝜑↔𝜓⋀𝜓𝜑Modus ponens id, 6156iba
6162↔⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗𝜑] into ancom
6163→↔⋀𝜓𝜑⋀𝜑𝜓→𝜑↔⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
6164→𝜑↔⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6162, 6163
6165↔→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑Subs [𝜒↗⋀𝜓𝜑] into pm5.74
6166→↔→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑Subs [𝜑↗→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜓𝜑] into biimp
6167→→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑Modus ponens 6165, 6166
6168↔→𝜑𝜓→𝜑⋀𝜓𝜑Modus ponens iba, 6167ancrb
6169↔→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓Subs [𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74
6170→↔→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓] into biimp
6171→→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓Modus ponens 6169, 6170
6172↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓Modus ponens 6164, 6171
6173→↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
6174→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓Modus ponens 6172, 6173
6175→↔→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into biimp
6176→→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
6177→→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓Modus ponens 6174, 6176
6178→→→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2
6179→→→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 6177, 6178
6180→→𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens ancr, 6179ancl
6181→↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1
6182↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑Modus ponens 6172, 6181
6183→↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into biimp
6184→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑Modus ponens 6182, 6183
6185→↔→𝜑𝜓→𝜑⋀𝜓𝜑↔→𝜑⋀𝜓𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into bicom1
6186↔→𝜑⋀𝜓𝜑→𝜑𝜓Modus ponens ancrb, 6185
6187→↔→𝜑⋀𝜓𝜑→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into biimp
6188→→𝜑⋀𝜓𝜑→𝜑𝜓Modus ponens 6186, 6187
6189→→→𝜑⋀𝜓𝜑→𝜑𝜓→→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜓𝜑→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into ax-1
6190→→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓Modus ponens 6188, 6189
6191→→→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓→→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2
6192→→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 6190, 6191
6193→→𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 6184, 6192
6194→→→𝜑𝜓→𝜑⋀𝜑𝜓→→→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into impbi
6195→→→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens ancl, 6194
6196↔→𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 6193, 6195anclb
6197↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜒↗⋀𝜑𝜓] into pm5.74
6198→↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓Subs [𝜑↗→𝜑↔𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜑𝜓] into bicom1
6199↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓Modus ponens 6197, 6198
6200→↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓→↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜑⋀𝜑𝜓, 𝜓↗→𝜑↔𝜓⋀𝜑𝜓] into biimp
6201→↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓Modus ponens 6199, 6200
6202→𝜑↔𝜓⋀𝜑𝜓Modus ponens anclb, 6201ibar
6203→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into ibar
6204→↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6205→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens pm4.76, 6204
6206↔→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into pm5.74
6207→↔→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp
6208→→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Modus ponens 6206, 6207
6209↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Modus ponens 6203, 6208
6210↔→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into pm5.74
6211→↔→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒] into biimp
6212→→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 6210, 6211
6213↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 6205, 6212
6214→↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into biimp
6215→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 6213, 6214
6216→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp
6217→→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
6218→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 6215, 6217
6219→→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2
6220→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 6218, 6219
6221→↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into bicom1
6222↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Modus ponens 6213, 6221
6223→↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp
6224→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒Modus ponens 6222, 6223
6225→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into bicom1
6226↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 6209, 6225
6227→↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into biimp
6228→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 6226, 6227
6229→→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-1
6230→→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 6228, 6229
6231→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
6232→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 6230, 6231
6233→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 6224, 6232
6234→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into impbi
6235→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 5610, 6234
6236↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 6233, 6235
6237↔→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into pm5.74
6238→↔→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒] into bicom1
6239↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 6237, 6238
6240→↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒] into biimp
6241→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 6239, 6240
6242→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 6236, 6241pm5.44
6243↔↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into bicom
6244→↔↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→𝜑⋀𝜓𝜒→𝜑𝜒] into biimp
6245→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒Modus ponens 6243, 6244
6246→→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
6247→→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒Modus ponens 6245, 6246
6248→→→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜒↗↔→𝜑⋀𝜓𝜒→𝜑𝜒] into ax-2
6249→→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒Modus ponens 6247, 6248
6250→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒Modus ponens pm5.44, 6249
6251↔↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜒] into bicom
6252→↔↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗↔→𝜑𝜒→𝜑⋀𝜓𝜒] into biimp
6253→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 6251, 6252
6254→→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6255→→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 6253, 6254
6256→→→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜒↗↔→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2
6257→→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 6255, 6256
6258→𝜑↔𝜒⋀𝜑𝜒Subs [𝜓↗𝜒] into ibar
6259→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒Subs [𝜑↗↔𝜒⋀𝜑𝜒] into ax-1
6260→→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒→𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒Subs [𝜑↗→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒, 𝜓↗𝜑] into ax-1
6261→𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒Modus ponens 6259, 6260
6262→→𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒→→𝜑↔𝜒⋀𝜑𝜒→𝜑→𝜓↔𝜒⋀𝜑𝜒Subs [𝜓↗↔𝜒⋀𝜑𝜒, 𝜒↗→𝜓↔𝜒⋀𝜑𝜒] into ax-2
6263→→𝜑↔𝜒⋀𝜑𝜒→𝜑→𝜓↔𝜒⋀𝜑𝜒Modus ponens 6261, 6262
6264→𝜑→𝜓↔𝜒⋀𝜑𝜒Modus ponens 6258, 6263
6265↔→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74
6266→↔→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒Subs [𝜑↗→𝜓↔𝜒⋀𝜑𝜒, 𝜓↗↔→𝜓𝜒→𝜓⋀𝜑𝜒] into biimp
6267→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒Modus ponens 6265, 6266
6268→→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒Subs [𝜑↗→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒, 𝜓↗𝜑] into ax-1
6269→𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒Modus ponens 6267, 6268
6270→→𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→→𝜑→𝜓↔𝜒⋀𝜑𝜒→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒Subs [𝜓↗→𝜓↔𝜒⋀𝜑𝜒, 𝜒↗↔→𝜓𝜒→𝜓⋀𝜑𝜒] into ax-2
6271→→𝜑→𝜓↔𝜒⋀𝜑𝜒→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒Modus ponens 6269, 6270
6272→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒Modus ponens 6264, 6271
6273↔→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓⋀𝜑𝜒] into pm5.74
6274→↔→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒Subs [𝜑↗→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒, 𝜓↗↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒] into biimp
6275→→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒Modus ponens 6273, 6274
6276↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒Modus ponens 6272, 6275pm5.42
6277→→𝜑→𝜓⋀𝜑𝜓→→𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜒↗⋀𝜑𝜓] into ax-2
6278→↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑↔𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜑𝜓] into biimp
6279→→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 6197, 6278
6280→↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into biimp
6281→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒Modus ponens pm5.42, 6280anc2l
6282→𝜑→𝜒⋀𝜒𝜑Subs [𝜓↗𝜒] into pm3.21
6283→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑Subs [𝜑↗→𝜒⋀𝜒𝜑] into ax-1
6284→→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑Subs [𝜑↗→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑, 𝜓↗𝜑] into ax-1
6285→𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑Modus ponens 6283, 6284
6286→→𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑→→𝜑→𝜒⋀𝜒𝜑→𝜑→𝜓→𝜒⋀𝜒𝜑Subs [𝜓↗→𝜒⋀𝜒𝜑, 𝜒↗→𝜓→𝜒⋀𝜒𝜑] into ax-2
6287→→𝜑→𝜒⋀𝜒𝜑→𝜑→𝜓→𝜒⋀𝜒𝜑Modus ponens 6285, 6286
6288→𝜑→𝜓→𝜒⋀𝜒𝜑Modus ponens 6282, 6287
6289→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜒𝜑] into ax-2
6290→→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑Subs [𝜑↗→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑, 𝜓↗𝜑] into ax-1
6291→𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑Modus ponens 6289, 6290
6292→→𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→→𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑Subs [𝜓↗→𝜓→𝜒⋀𝜒𝜑, 𝜒↗→→𝜓𝜒→𝜓⋀𝜒𝜑] into ax-2
6293→→𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑Modus ponens 6291, 6292
6294→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑Modus ponens 6288, 6293
6295→→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜒𝜑Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓⋀𝜒𝜑] into ax-2
6296→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜒𝜑Modus ponens 6294, 6295anc2r
6297→→⋀𝜑𝜓𝜑↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑Subs [𝜑↗→⋀𝜑𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into iba
6298↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑Modus ponens simpl, 6297
6299↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑Subs [𝜓↗⋀𝜑𝜓] into dfbi2
6300→↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into bicom1
6301↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓Modus ponens 6299, 6300
6302→↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp
6303→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓Modus ponens 6301, 6302
6304→↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into biimp
6305→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑Modus ponens 6298, 6304
6306→→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓Subs [𝜑↗→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into ax-1
6307→→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓Modus ponens 6303, 6306
6308→→→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜒↗↔𝜑⋀𝜑𝜓] into ax-2
6309→→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens 6307, 6308
6310→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens 6305, 6309
6311→↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1
6312→↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into biimp
6313→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑Modus ponens 6299, 6312
6314→↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into bicom1
6315↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓Modus ponens 6298, 6314
6316→↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
6317→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓Modus ponens 6315, 6316
6318→→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓Subs [𝜑↗→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1
6319→↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓Modus ponens 6317, 6318
6320→→↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2
6321→→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 6319, 6320
6322→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 6313, 6321
6323→→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into impbi
6324→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens 6310, 6323
6325↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens 6322, 6324
6326→↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp
6327→↔→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
6328→→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
6329→→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens 6310, 6328
6330→→→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗↔𝜑⋀𝜑𝜓] into ax-2
6331→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens 6329, 6330
6332→→𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens ancl, 6331
6333→↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1
6334↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 6325, 6333
6335→↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
6336→↔→𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1
6337↔→𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens anclb, 6336
6338→↔→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp
6339→→→𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1
6340→↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 6193, 6339
6341→→↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
6342→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 6340, 6341
6343→↔𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 6322, 6342
6344→→→𝜑𝜓↔𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into impbi
6345→→↔𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens 6332, 6344
6346↔→𝜑𝜓↔𝜑⋀𝜑𝜓Modus ponens 6343, 6345pm4.71
6347→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜑𝜓] into id
6348→↔⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1
6349→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑Modus ponens ancom, 6348
6350↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74
6351→↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp
6352→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6350, 6351
6353↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6347, 6352
6354↔→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.74
6355→↔→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into biimp
6356→→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Modus ponens 6354, 6355
6357↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Modus ponens 6349, 6356
6358→↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into biimp
6359→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Modus ponens 6357, 6358
6360→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp
6361→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6353, 6360
6362→→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓𝜑] into ax-1
6363→→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Modus ponens 6359, 6362
6364→→→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into ax-2
6365→→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Modus ponens 6363, 6364
6366→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Modus ponens 6361, 6365
6367→↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into bicom1
6368↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6357, 6367
6369→↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp
6370→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6368, 6369
6371→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into bicom1
6372↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑Modus ponens 6353, 6371
6373→↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓𝜑] into biimp
6374→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑Modus ponens 6372, 6373
6375→→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑Subs [𝜑↗→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into ax-1
6376→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑Modus ponens 6374, 6375
6377→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔𝜑⋀𝜑𝜓𝜑] into ax-2
6378→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑Modus ponens 6376, 6377
6379→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑Modus ponens 6370, 6378
6380→→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into impbi
6381→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Modus ponens 6366, 6380
6382↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Modus ponens 6379, 6381
6383↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into pm5.74
6384→↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into bicom1
6385↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6383, 6384
6386→↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Subs [𝜑↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑] into biimp
6387→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6385, 6386
6388→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6382, 6387
6389→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜑] into id
6390→↔⋀𝜑𝜓⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into bicom1
6391→↔⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1
6392→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6162, 6391
6393↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into pm5.74
6394→↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp
6395→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Modus ponens 6393, 6394
6396↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Modus ponens 6389, 6395
6397↔→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74
6398→↔→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into biimp
6399→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6397, 6398
6400↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6392, 6399
6401→↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into biimp
6402→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6400, 6401
6403→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp
6404→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Modus ponens 6396, 6403
6405→→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑𝜑] into ax-1
6406→→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6402, 6405
6407→→→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜒↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into ax-2
6408→→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6406, 6407
6409→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6404, 6408
6410→↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into bicom1
6411↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Modus ponens 6400, 6410
6412→↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp
6413→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑Modus ponens 6411, 6412
6414→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into bicom1
6415↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑Modus ponens 6396, 6414
6416→↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑𝜑] into biimp
6417→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑Modus ponens 6415, 6416
6418→→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑Subs [𝜑↗→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into ax-1
6419→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑Modus ponens 6417, 6418
6420→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜒↗→↔𝜑⋀𝜓𝜑𝜑] into ax-2
6421→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑Modus ponens 6419, 6420
6422→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑Modus ponens 6413, 6421
6423→→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into impbi
6424→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6409, 6423
6425↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6422, 6424
6426↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74
6427→↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into bicom1
6428↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓Modus ponens 6426, 6427
6429→↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓Subs [𝜑↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓] into biimp
6430→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓Modus ponens 6428, 6429
6431→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓Modus ponens 6425, 6430
6432→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into impbi
6433→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6388, 6432
6434↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6431, 6433
6435→↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp
6436→↔→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp
6437→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1
6438→→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6388, 6437
6439→→→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓, 𝜒↗↔𝜑⋀𝜓𝜑] into ax-2
6440→→→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6438, 6439
6441→→𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6332, 6440
6442→↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into bicom1
6443↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓Modus ponens 6434, 6442
6444→↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp
6445→↔→𝜑𝜓↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1
6446↔↔𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens pm4.71, 6445
6447→↔↔𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp
6448→→↔𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1
6449→↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 6343, 6448
6450→→↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
6451→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓Modus ponens 6449, 6450
6452→↔𝜑⋀𝜓𝜑→𝜑𝜓Modus ponens 6431, 6451
6453→→→𝜑𝜓↔𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into impbi
6454→→↔𝜑⋀𝜓𝜑→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6441, 6453
6455↔→𝜑𝜓↔𝜑⋀𝜓𝜑Modus ponens 6452, 6454pm4.71r
6456↔→𝜑𝜑↔𝜑⋀𝜑𝜑Subs [𝜓↗𝜑] into pm4.71
6457→↔→𝜑𝜑↔𝜑⋀𝜑𝜑→→𝜑𝜑↔𝜑⋀𝜑𝜑Subs [𝜑↗→𝜑𝜑, 𝜓↗↔𝜑⋀𝜑𝜑] into biimp
6458→→𝜑𝜑↔𝜑⋀𝜑𝜑Modus ponens 6456, 6457
6459↔𝜑⋀𝜑𝜑Modus ponens id, 6458pm4.24
6460→↔𝜑⋀𝜑𝜑↔⋀𝜑𝜑𝜑Subs [𝜓↗⋀𝜑𝜑] into bicom1
6461↔⋀𝜑𝜑𝜑Modus ponens pm4.24, 6460anidm
6462↔⋀𝜓𝜓𝜓Subs [𝜑↗𝜓] into anidm
6463→↔⋀𝜓𝜓𝜓→𝜑↔⋀𝜓𝜓𝜓Subs [𝜑↗↔⋀𝜓𝜓𝜓, 𝜓↗𝜑] into ax-1
6464→𝜑↔⋀𝜓𝜓𝜓Modus ponens 6462, 6463
6465↔→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓Subs [𝜓↗⋀𝜓𝜓, 𝜒↗𝜓] into pm5.74
6466→↔→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓→→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓Subs [𝜑↗→𝜑↔⋀𝜓𝜓𝜓, 𝜓↗↔→𝜑⋀𝜓𝜓→𝜑𝜓] into biimp
6467→→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓Modus ponens 6465, 6466
6468↔→𝜑⋀𝜓𝜓→𝜑𝜓Modus ponens 6464, 6467anidmdbi
6469↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒Subs [𝜒↗⋀𝜑𝜒] into impexp
6470→↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into bicom1
6471↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6469, 6470
6472→↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into biimp
6473→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6471, 6472
6474→→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
6475→→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6473, 6474
6476→→→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒, 𝜒↗→⋀𝜑𝜓⋀𝜑𝜒] into ax-2
6477→→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6475, 6476
6478→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens anc2l, 6477
6479→↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into bicom1
6480→↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into biimp
6481→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒Modus ponens 6469, 6480
6482→↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into bicom1
6483↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Modus ponens pm5.42, 6482
6484→↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into biimp
6485→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Modus ponens 6483, 6484
6486→→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into ax-1
6487→→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Modus ponens 6485, 6486
6488→→→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
6489→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Modus ponens 6487, 6488
6490→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒Modus ponens 6481, 6489
6491→→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into impbi
6492→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6478, 6491
6493↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6490, 6492imdistan
6494→→𝜑↔𝜒⋀𝜑𝜒→⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒Subs [𝜑↗→𝜑↔𝜒⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
6495→⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒Modus ponens 6258, 6494
6496→→⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒→→⋀𝜑𝜓𝜑→⋀𝜑𝜓↔𝜒⋀𝜑𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗↔𝜒⋀𝜑𝜒] into ax-2
6497→→⋀𝜑𝜓𝜑→⋀𝜑𝜓↔𝜒⋀𝜑𝜒Modus ponens 6495, 6496
6498→⋀𝜑𝜓↔𝜒⋀𝜑𝜒Modus ponens simpl, 6497
6499↔→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74
6500→↔→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒→→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→⋀𝜑𝜓↔𝜒⋀𝜑𝜒, 𝜓↗↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒] into biimp
6501→→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6499, 6500
6502↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6498, 6501pm5.3
6503↔↔𝜓𝜒↔¬𝜓¬𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into notbi
6504→↔↔𝜓𝜒↔¬𝜓¬𝜒→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒Subs [𝜑↗↔↔𝜓𝜒↔¬𝜓¬𝜒, 𝜓↗𝜑] into ax-1
6505→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒Modus ponens 6503, 6504
6506↔→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔¬𝜓¬𝜒] into pm5.74
6507→↔→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜑↗→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒] into biimp
6508→→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6506, 6507
6509↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6505, 6508
6510↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒Subs [𝜓↗¬𝜓, 𝜒↗¬𝜒] into pm5.74
6511↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜒] into notbi
6512→↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6513→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6511, 6512
6514→↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into biimp
6515→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒Modus ponens 6510, 6514
6516→→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into ax-1
6517→→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6513, 6516
6518→→→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6519→→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6517, 6518
6520→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6515, 6519
6521→↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6522↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒Modus ponens 6511, 6521
6523→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into biimp
6524→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒Modus ponens 6522, 6523
6525→↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into bicom1
6526↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6510, 6525
6527→↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp
6528→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6526, 6527
6529→→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜑↗→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6530→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6528, 6529
6531→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜒↗→𝜑↔¬𝜓¬𝜒] into ax-2
6532→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6530, 6531
6533→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6524, 6532
6534→→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6535→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6520, 6534
6536↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6533, 6535
6537→↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6538→↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp
6539→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6509, 6538
6540→→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
6541→→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6520, 6540
6542→→→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6543→→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6541, 6542
6544→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6539, 6543
6545→↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6546↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Modus ponens 6536, 6545
6547→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp
6548→↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into bicom1
6549↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒Modus ponens 6509, 6548
6550→↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
6551→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒Modus ponens 6549, 6550
6552→→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6553→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒Modus ponens 6551, 6552
6554→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
6555→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒Modus ponens 6553, 6554
6556→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒Modus ponens 6533, 6555
6557→→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6558→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6544, 6557
6559↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6556, 6558
6560↔⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜓↗𝜒] into df-an
6561→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒] into id
6562→↔⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1
6563→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6560, 6562
6564↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜒] into pm5.74
6565→↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp
6566→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Modus ponens 6564, 6565
6567↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Modus ponens 6561, 6566
6568↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜒, 𝜒↗¬→𝜑¬𝜒] into pm5.74
6569→↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into biimp
6570→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6568, 6569
6571↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6563, 6570
6572→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into biimp
6573→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6571, 6572
6574→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp
6575→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Modus ponens 6567, 6574
6576→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into ax-1
6577→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6573, 6576
6578→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜒↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into ax-2
6579→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6577, 6578
6580→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6575, 6579
6581→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into bicom1
6582↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Modus ponens 6571, 6581
6583→↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp
6584→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒Modus ponens 6582, 6583
6585→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into bicom1
6586↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Modus ponens 6567, 6585
6587→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into biimp
6588→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Modus ponens 6586, 6587
6589→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Subs [𝜑↗→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into ax-1
6590→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Modus ponens 6588, 6589
6591→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜒↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into ax-2
6592→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Modus ponens 6590, 6591
6593→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓Modus ponens 6584, 6592
6594→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into impbi
6595→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6580, 6594
6596↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6593, 6595
6597↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜒] into pm5.74
6598→↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into bicom1
6599↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6597, 6598
6600→↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6601→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6599, 6600
6602→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6596, 6601
6603→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into id
6604→↔⋀𝜑𝜒¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒] into bicom1
6605↔¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6560, 6604
6606→↔¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1
6607→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6605, 6606
6608↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜒] into pm5.74
6609→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp
6610→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 6608, 6609
6611↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 6603, 6610
6612↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74
6613→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into biimp
6614→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6612, 6613
6615↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6607, 6614
6616→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into biimp
6617→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6615, 6616
6618→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp
6619→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 6611, 6618
6620→→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1
6621→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6617, 6620
6622→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into ax-2
6623→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6621, 6622
6624→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6619, 6623
6625→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into bicom1
6626↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 6615, 6625
6627→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp
6628→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 6626, 6627
6629→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into bicom1
6630↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6611, 6629
6631→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6632→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6630, 6631
6633→→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into ax-1
6634→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6632, 6633
6635→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into ax-2
6636→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6634, 6635
6637→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6628, 6636
6638→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into impbi
6639→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6624, 6638
6640↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6637, 6639
6641↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜒] into pm5.74
6642→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into bicom1
6643↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6641, 6642
6644→↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒] into biimp
6645→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6643, 6644
6646→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6640, 6645
6647→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into impbi
6648→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6602, 6647
6649↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6646, 6648
6650↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒] into bicom
6651→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into id
6652→↔⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1
6653→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens df-an, 6652
6654↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜓] into pm5.74
6655→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp
6656→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6654, 6655
6657↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6651, 6656
6658↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜓] into pm5.74
6659→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into biimp
6660→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens 6658, 6659
6661↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens 6653, 6660
6662→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into biimp
6663→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens 6661, 6662
6664→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp
6665→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6657, 6664
6666→→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1
6667→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens 6663, 6666
6668→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into ax-2
6669→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens 6667, 6668
6670→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens 6665, 6669
6671→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into bicom1
6672↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6661, 6671
6673→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp
6674→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓Modus ponens 6672, 6673
6675→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into bicom1
6676↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6657, 6675
6677→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6678→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6676, 6677
6679→→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into ax-1
6680→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6678, 6679
6681→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into ax-2
6682→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6680, 6681
6683→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6674, 6682
6684→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into impbi
6685→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens 6670, 6684
6686↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Modus ponens 6683, 6685
6687↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜓] into pm5.74
6688→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into bicom1
6689↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Modus ponens 6687, 6688
6690→↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Subs [𝜑↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp
6691→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Modus ponens 6689, 6690
6692→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Modus ponens 6686, 6691
6693→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into id
6694→↔¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into ax-1
6695→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens pm4.63, 6694
6696↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜓] into pm5.74
6697→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp
6698→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 6696, 6697
6699↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 6693, 6698
6700↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜑𝜓] into pm5.74
6701→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into biimp
6702→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 6700, 6701
6703↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 6695, 6702
6704→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into biimp
6705→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 6703, 6704
6706→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp
6707→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 6699, 6706
6708→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6709→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 6705, 6708
6710→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into ax-2
6711→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 6709, 6710
6712→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 6707, 6711
6713→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into bicom1
6714↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 6703, 6713
6715→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp
6716→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 6714, 6715
6717→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into bicom1
6718↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6699, 6717
6719→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6720→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6718, 6719
6721→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into ax-1
6722→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6720, 6721
6723→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6724→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6722, 6723
6725→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6716, 6724
6726→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into impbi
6727→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 6712, 6726
6728↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Modus ponens 6725, 6727
6729↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜓] into pm5.74
6730→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into bicom1
6731↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6729, 6730
6732→↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6733→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6731, 6732
6734→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6728, 6733
6735→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into impbi
6736→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Modus ponens 6692, 6735
6737↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Modus ponens 6734, 6736
6738↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜓] into bicom
6739→↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6740→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6738, 6739
6741→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp
6742→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1
6743→↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6740, 6742
6744→→↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6745→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6743, 6744
6746→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6692, 6745
6747→↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6748↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓Modus ponens 6738, 6747
6749→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp
6750→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓Modus ponens 6748, 6749
6751→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into bicom1
6752↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6737, 6751
6753→↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6754→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6755→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6734, 6754
6756→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜒↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-2
6757→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6755, 6756
6758→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6750, 6757
6759→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6760→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6746, 6759
6761↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6758, 6760
6762→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6763→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6764→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6650, 6763
6765→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1
6766→↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6746, 6765
6767→→↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6768→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6766, 6767
6769→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6764, 6768
6770→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6771↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Modus ponens 6761, 6770
6772→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6773→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into bicom1
6774↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6650, 6773
6775→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6776→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6774, 6775
6777→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6778→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6776, 6777
6779→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜒↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-2
6780→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6778, 6779
6781→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6758, 6780
6782→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6783→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6769, 6782
6784↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6781, 6783
6785→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6786→↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6787→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1
6788→↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6769, 6787
6789→→↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6790→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6788, 6789
6791→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6602, 6790
6792→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6793↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Modus ponens 6784, 6792
6794→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6795→↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into bicom1
6796↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6649, 6795
6797→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into biimp
6798→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6799→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6646, 6798
6800→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜒↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-2
6801→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6799, 6800
6802→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6781, 6801
6803→→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6804→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6791, 6803
6805↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Modus ponens 6802, 6804
6806→↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6807↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6805, 6806
6808→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into biimp
6809→↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6810→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
6811→→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6802, 6810
6812→→→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜒↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-2
6813→→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6811, 6812
6814→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6544, 6813
6815→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into bicom1
6816→↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6817→↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6818↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒Modus ponens 6559, 6817
6819→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
6820→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1
6821→↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒Modus ponens 6556, 6820
6822→→↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
6823→→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒Modus ponens 6821, 6822
6824→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒Modus ponens 6791, 6823
6825→→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into impbi
6826→→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6814, 6825
6827↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒Modus ponens 6824, 6826pm5.32
6828→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into idd
6829→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6830→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
6831→⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6829, 6830
6832→→⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6833→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6831, 6832
6834→→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜓𝜒] into ax-2
6835→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6828, 6834
6836→→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
6837→⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6835, 6836
6838→→⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6839→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6837, 6838
6840→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-1
6841→¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6829, 6840
6842→→¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6843→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6841, 6842
6844→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 5017, 6843
6845→→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6846→𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6844, 6845
6847→→𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6848→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6846, 6847
6849→→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
6850→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6848, 6849
6851→→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6852→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6850, 6851
6853→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 5023, 6852
6854→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into pm2.27
6855→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒] into ax-1
6856→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒Modus ponens 6854, 6855
6857→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6858→→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
6859→𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6857, 6858
6860→→𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6861→→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6859, 6860
6862→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6853, 6861
6863→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into imim2
6864→→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6865→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6863, 6864
6866→→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2
6867→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6865, 6866
6868→→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-1
6869→𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6867, 6868
6870→→𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2
6871→→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6869, 6870
6872→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6856, 6871
6873→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2
6874→→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1
6875→𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6873, 6874
6876→→𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2
6877→→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6875, 6876
6878→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6872, 6877
6879→→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2
6880→→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6878, 6879
6881→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6862, 6880
6882→→𝜑𝜓→𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓] into ax-1
6883→→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
6884→→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓Modus ponens 6882, 6883
6885→→→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓→𝜑𝜓] into ax-2
6886→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓Modus ponens 6884, 6885
6887→→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2
6888→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Modus ponens 6881, 6887
6889→→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6890→→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Modus ponens 6888, 6889
6891→→→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜑𝜓, 𝜒↗→𝜓→𝜒⋀𝜓𝜒] into ax-2
6892→→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Modus ponens 6890, 6891
6893→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Modus ponens 6882, 6892
6894→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗⋀𝜓𝜒] into pm2.27
6895→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6896→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒Modus ponens 6894, 6895
6897→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6898→→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6899→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒Modus ponens 6897, 6898
6900→→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜓→𝜒⋀𝜓𝜒] into ax-2
6901→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒Modus ponens 6899, 6900
6902→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒Modus ponens 6893, 6901
6903→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into imim2
6904→→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6905→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 6903, 6904
6906→→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2
6907→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 6905, 6906
6908→→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6909→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 6907, 6908
6910→→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2
6911→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 6909, 6910
6912→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 6896, 6911
6913→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
6914→→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6915→→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 6913, 6914
6916→→→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2
6917→→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 6915, 6916
6918→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 6912, 6917
6919→→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2
6920→→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 6918, 6919
6921→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 6902, 6920
6922→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗⋀𝜓𝜒] into pm2.27
6923→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6924→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒Modus ponens 6922, 6923
6925→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜒→𝜓⋀𝜓𝜒] into ax-1
6926→→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6927→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 6925, 6926
6928→→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→𝜒→𝜓⋀𝜓𝜒] into ax-2
6929→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 6927, 6928
6930→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 6921, 6929
6931→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into imim2
6932→→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-1
6933→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6931, 6932
6934→→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2
6935→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6933, 6934
6936→→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6937→→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6935, 6936
6938→→→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2
6939→→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6937, 6938
6940→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒Modus ponens 6924, 6939
6941→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2
6942→→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6943→→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒Modus ponens 6941, 6942
6944→→→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒] into ax-2
6945→→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒Modus ponens 6943, 6944
6946→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒Modus ponens 6940, 6945
6947→→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→𝜒⋀𝜓𝜒] into ax-2
6948→→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒Modus ponens 6946, 6947
6949→𝜓→→𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓] into ax-1
6950→→𝜓→→𝜑𝜓𝜓→𝜓→𝜓→→𝜑𝜓𝜓Subs [𝜑↗→𝜓→→𝜑𝜓𝜓] into ax-1
6951→𝜓→𝜓→→𝜑𝜓𝜓Modus ponens 6949, 6950
6952→→𝜓→𝜓→→𝜑𝜓𝜓→→𝜓𝜓→𝜓→→𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜒↗→→𝜑𝜓𝜓] into ax-2
6953→→𝜓𝜓→𝜓→→𝜑𝜓𝜓Modus ponens 6951, 6952
6954→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2
6955→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6893, 6954
6956→→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1
6957→𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6955, 6956
6958→→𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓𝜓→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓𝜓, 𝜒↗→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2
6959→→𝜓→→𝜑𝜓𝜓→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6957, 6958
6960→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒] into ax-1
6961→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒Modus ponens 6894, 6960
6962→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6963→→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1
6964→𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6962, 6963
6965→→𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2
6966→→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6964, 6965
6967→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒Modus ponens 6881, 6966
6968→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2
6969→→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6970→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6968, 6969
6971→→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6972→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6970, 6971
6973→→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
6974→𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6972, 6973
6975→→𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6976→→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6974, 6975
6977→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6961, 6976
6978→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6979→→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
6980→𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6978, 6979
6981→→𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6982→→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6980, 6981
6983→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6977, 6982
6984→→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6985→→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6983, 6984
6986→→𝜒→𝜓𝜒→𝜒→𝜒→𝜓𝜒Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗𝜒] into ax-1
6987→𝜒→𝜒→𝜓𝜒Modus ponens 5362, 6986
6988→→𝜒→𝜒→𝜓𝜒→→𝜒𝜒→𝜒→𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2
6989→→𝜒𝜒→𝜒→𝜓𝜒Modus ponens 6987, 6988
6990→→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6991→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 6853, 6990
6992→→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6993→𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 6991, 6992
6994→→𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
6995→→𝜒→𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 6993, 6994
6996→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 5362, 6995
6997↔⋀𝜒𝜓¬→𝜒¬𝜓Subs [𝜑↗𝜒] into df-an
6998→→𝜓→𝜒𝜓→¬¬𝜓→𝜓→𝜒𝜓Subs [𝜑↗→𝜓→𝜒𝜓, 𝜓↗¬¬𝜓] into ax-1
6999→¬¬𝜓→𝜓→𝜒𝜓Modus ponens 5350, 6998
7000→→¬¬𝜓→𝜓→𝜒𝜓→→¬¬𝜓𝜓→¬¬𝜓→𝜒𝜓Subs [𝜑↗¬¬𝜓, 𝜒↗→𝜒𝜓] into ax-2
7001→→¬¬𝜓𝜓→¬¬𝜓→𝜒𝜓Modus ponens 6999, 7000
7002→¬¬𝜓→𝜒𝜓Modus ponens 570, 7001
7003→→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7004→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6996, 7003
7005→→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1
7006→¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7004, 7005
7007→→¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7008→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7006, 7007
7009→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7002, 7008
7010→𝜒→¬¬𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗¬¬𝜓] into ax-1
7011→→𝜒→¬¬𝜓𝜒→𝜒→𝜒→¬¬𝜓𝜒Subs [𝜑↗→𝜒→¬¬𝜓𝜒, 𝜓↗𝜒] into ax-1
7012→𝜒→𝜒→¬¬𝜓𝜒Modus ponens 7010, 7011
7013→→𝜒→𝜒→¬¬𝜓𝜒→→𝜒𝜒→𝜒→¬¬𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→¬¬𝜓𝜒] into ax-2
7014→→𝜒𝜒→𝜒→¬¬𝜓𝜒Modus ponens 7012, 7013
7015→→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7016→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7009, 7015
7017→→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7018→𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7016, 7017
7019→→𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7020→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7018, 7019
7021→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7010, 7020
7022→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒] into notnot
7023→→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1
7024→¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7022, 7023
7025→→¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7026→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7024, 7025
7027→→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7028→𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7026, 7027
7029→→𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7030→→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7028, 7029
7031→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7021, 7030
7032→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-3
7033→→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓, 𝜓↗𝜒] into ax-1
7034→𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓Modus ponens 7032, 7033
7035→→𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓] into ax-2
7036→→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓Modus ponens 7034, 7035
7037→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓Modus ponens 7031, 7036
7038→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒] into id
7039→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7040→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7041→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7039, 7040
7042→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7043→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7041, 7042
7044→→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓Subs [𝜑↗𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜓] into ax-2
7045→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓Modus ponens 7037, 7044
7046→→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓Subs [𝜑↗→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7047→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓Modus ponens 7045, 7046
7048→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒¬𝜓] into ax-2
7049→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓Modus ponens 7047, 7048
7050→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓Modus ponens 7039, 7049
7051→¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗¬→𝜒¬𝜓] into id
7052→→¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗→¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7053→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 7051, 7052
7054→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗¬→𝜒¬𝜓] into notnotr
7055→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7056→→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Subs [𝜑↗→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
7057→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Modus ponens 7055, 7056
7058→→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓] into ax-2
7059→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Modus ponens 7057, 7058
7060→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Modus ponens 7054, 7059
7061→→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓, 𝜒↗¬→𝜒¬𝜓] into ax-2
7062→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Modus ponens 7053, 7061
7063→→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
7064→¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Modus ponens 7062, 7063
7065→→¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓] into ax-2
7066→→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓Modus ponens 7064, 7065
7067→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
7068→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7069→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7067, 7068
7070→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7071→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7069, 7070
7072→→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜒¬𝜓] into ax-2
7073→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 7060, 7072
7074→→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7075→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 7073, 7074
7076→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓] into ax-2
7077→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 7075, 7076
7078→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 7067, 7077
7079→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓Subs [𝜑↗¬¬→𝜒¬𝜓, 𝜓↗→𝜒¬𝜓] into ax-3
7080→→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7081→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓Modus ponens 7079, 7080
7082→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜒↗→→𝜒¬𝜓¬¬→𝜒¬𝜓] into ax-2
7083→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓Modus ponens 7081, 7082
7084→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓Modus ponens 7078, 7083
7085→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜒¬𝜓, 𝜒↗¬¬→𝜒¬𝜓] into ax-2
7086→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓Modus ponens 7084, 7085
7087→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓Modus ponens 7050, 7086
7088→→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-3
7089→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7087, 7088
7090→↔⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓¬→𝜒¬𝜓Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into biimp
7091→⋀𝜒𝜓¬→𝜒¬𝜓Modus ponens 6997, 7090
7092→→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1
7093→⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7089, 7092
7094→→⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7095→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7093, 7094
7096→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7091, 7095
7097→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜒𝜓] into ax-1
7098→→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
7099→→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓Modus ponens 7097, 7098
7100→→→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜒𝜓→𝜑𝜓] into ax-2
7101→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓Modus ponens 7099, 7100
7102→→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2
7103→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒Modus ponens 7096, 7102
7104→→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒Subs [𝜑↗→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7105→→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒Modus ponens 7103, 7104
7106→→→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜒𝜓→𝜑𝜓, 𝜒↗→⋀𝜒𝜓⋀𝜓𝜒] into ax-2
7107→→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒Modus ponens 7105, 7106
7108→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒Modus ponens 7097, 7107
7109→⋀𝜒𝜓⋀𝜒𝜓Subs [𝜑↗⋀𝜒𝜓] into id
7110→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
7111→→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓, 𝜓↗⋀𝜒𝜓] into ax-1
7112→⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓Modus ponens 7110, 7111
7113→→⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→→⋀𝜒𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓Subs [𝜑↗⋀𝜒𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜒𝜓] into ax-2
7114→→⋀𝜒𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓Modus ponens 7112, 7113
7115→→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜓𝜒] into ax-2
7116→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7108, 7115
7117→→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1
7118→⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7116, 7117
7119→→⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→→𝜑𝜓⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7120→→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7118, 7119
7121→↔⋀𝜒𝜓¬→𝜒¬𝜓↔¬→𝜒¬𝜓⋀𝜒𝜓Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into bicom1
7122↔¬→𝜒¬𝜓⋀𝜒𝜓Modus ponens 6997, 7121
7123→↔¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓⋀𝜒𝜓Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓] into biimp
7124→¬→𝜒¬𝜓⋀𝜒𝜓Modus ponens 7122, 7123
7125→→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-1
7126→¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7096, 7125
7127→→¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7128→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7126, 7127
7129→𝜒→𝜓¬→𝜒¬𝜓Subs [𝜑↗𝜒] into pm3.2im
7130→→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-1
7131→𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7089, 7130
7132→→𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7133→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7131, 7132
7134→→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7135→𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7133, 7134
7136→→𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓¬→𝜒¬𝜓, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7137→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7135, 7136
7138→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7139→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒Modus ponens 6854, 7138
7140→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7141→→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7142→𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7140, 7141
7143→→𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7144→→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7142, 7143
7145→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 6996, 7144
7146→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into imim2
7147→→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7148→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 7146, 7147
7149→→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2
7150→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 7148, 7149
7151→→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7152→𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 7150, 7151
7153→→𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2
7154→→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 7152, 7153
7155→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒Modus ponens 7139, 7154
7156→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
7157→→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7158→𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7156, 7157
7159→→𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2
7160→→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7158, 7159
7161→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7155, 7160
7162→→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2
7163→→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7161, 7162
7164→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7145, 7163
7165→→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
7166→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 7164, 7165
7167→→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7168→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 7166, 7167
7169→→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2
7170→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 7168, 7169
7171→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7172→→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7173→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 7171, 7172
7174→→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2
7175→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 7173, 7174
7176→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 6921, 7175
7177→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
7178→→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7179→→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 7177, 7178
7180→→→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2
7181→→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 7179, 7180
7182→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒Modus ponens 7176, 7181
7183→→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2
7184→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒Modus ponens 7182, 7183
7185→𝜒→→𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into ax-1
7186→→𝜒→→𝜑𝜓𝜒→𝜒→𝜒→→𝜑𝜓𝜒Subs [𝜑↗→𝜒→→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
7187→𝜒→𝜒→→𝜑𝜓𝜒Modus ponens 7185, 7186
7188→→𝜒→𝜒→→𝜑𝜓𝜒→→𝜒𝜒→𝜒→→𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓𝜒] into ax-2
7189→→𝜒𝜒→𝜒→→𝜑𝜓𝜒Modus ponens 7187, 7188
7190→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
7191→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 6921, 7190
7192→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7193→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7191, 7192
7194→→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2
7195→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7193, 7194
7196→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7197→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒Modus ponens 6922, 7196
7198→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-1
7199→→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7200→𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7198, 7199
7201→→𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2
7202→→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7200, 7201
7203→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒Modus ponens 7164, 7202
7204→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2
7205→→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
7206→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7204, 7205
7207→→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7208→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7206, 7207
7209→→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7210→𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7208, 7209
7211→→𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7212→→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7210, 7211
7213→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7197, 7212
7214→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7215→→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7216→𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7214, 7215
7217→→𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7218→→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7216, 7217
7219→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7213, 7218
7220→→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7221→→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7219, 7220
7222→→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
7223→𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7004, 7222
7224→→𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒𝜓→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7225→→𝜓→𝜒𝜓→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7223, 7224
7226→→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
7227→¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 6991, 7226
7228→→¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7229→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 7227, 7228
7230→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒Modus ponens 5367, 7229
7231→→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7232→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7230, 7231
7233→→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
7234→𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7232, 7233
7235→→𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7236→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7234, 7235
7237→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 5375, 7236
7238→→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
7239→¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7022, 7238
7240→→¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7241→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7239, 7240
7242→→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7243→𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7241, 7242
7244→→𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7245→→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7243, 7244
7246→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7237, 7245
7247→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-3
7248→→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-1
7249→𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Modus ponens 7247, 7248
7250→→𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-2
7251→→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Modus ponens 7249, 7250
7252→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Modus ponens 7246, 7251
7253→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7254→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7255→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7253, 7254
7256→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7257→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7255, 7256
7258→→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒Subs [𝜑↗𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2
7259→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒Modus ponens 7252, 7258
7260→→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒Subs [𝜑↗→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7261→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒Modus ponens 7259, 7260
7262→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓¬𝜒] into ax-2
7263→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒Modus ponens 7261, 7262
7264→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒Modus ponens 7253, 7263
7265→→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7266→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 5416, 7265
7267→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7268→→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
7269→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Modus ponens 7267, 7268
7270→→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒] into ax-2
7271→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Modus ponens 7269, 7270
7272→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Modus ponens 5419, 7271
7273→→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
7274→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Modus ponens 7266, 7273
7275→→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
7276→¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Modus ponens 7274, 7275
7277→→¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒] into ax-2
7278→→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒Modus ponens 7276, 7277
7279→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
7280→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7281→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7279, 7280
7282→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7283→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7281, 7282
7284→→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
7285→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 7272, 7284
7286→→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7287→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 7285, 7286
7288→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2
7289→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 7287, 7288
7290→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 7279, 7289
7291→→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7292→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 5444, 7291
7293→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2
7294→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 7292, 7293
7295→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 7290, 7294
7296→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2
7297→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒Modus ponens 7295, 7296
7298→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒Modus ponens 7264, 7297
7299→→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3
7300→→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
7301→⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 6844, 7300
7302→→⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7303→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7301, 7302
7304→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
7305→→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
7306→→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓Modus ponens 7304, 7305
7307→→→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜓𝜒→𝜑𝜓] into ax-2
7308→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓Modus ponens 7306, 7307
7309→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2
7310→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒Modus ponens 6829, 7309
7311→→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7312→→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒Modus ponens 7310, 7311
7313→→→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜓𝜒→𝜑𝜓, 𝜒↗→⋀𝜓𝜒⋀𝜓𝜒] into ax-2
7314→→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒Modus ponens 7312, 7313
7315→→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7316→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒Modus ponens 5591, 7315
7317→→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜑→𝜓→𝜒⋀𝜓𝜒] into ax-2
7318→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒Modus ponens 7316, 7317
7319→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒Modus ponens 6893, 7318
7320→→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7321→→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Modus ponens 5593, 7320
7322→→→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒] into ax-2
7323→→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Modus ponens 7321, 7322
7324→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Modus ponens 7319, 7323
7325→→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜓𝜒] into ax-2
7326→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Modus ponens 7324, 7325
7327→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7328→→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7329→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒Modus ponens 7327, 7328
7330→→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜑→𝜒⋀𝜓𝜒] into ax-2
7331→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒Modus ponens 7329, 7330
7332→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒Modus ponens 5594, 7331
7333→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜑] into imim2
7334→→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7335→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 7333, 7334
7336→→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒] into ax-2
7337→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 7335, 7336
7338→→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7339→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 7337, 7338
7340→→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒] into ax-2
7341→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 7339, 7340
7342→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 6896, 7341
7343→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
7344→→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7345→→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒Modus ponens 7343, 7344
7346→→→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜒↗→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒] into ax-2
7347→→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒Modus ponens 7345, 7346
7348→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒Modus ponens 7342, 7347
7349→→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜑⋀𝜓𝜒] into ax-2
7350→→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒Modus ponens 7348, 7349
7351→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒Modus ponens 7332, 7350
7352→→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
7353→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 7351, 7352
7354→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7355→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 7353, 7354
7356→→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2
7357→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 7355, 7356
7358→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 7185, 7357
7359→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒Subs [𝜓↗⋀𝜓𝜒] into pm2.27
7360→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7361→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒Modus ponens 7359, 7360
7362→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7363→→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7364→𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 7362, 7363
7365→→𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2
7366→→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 7364, 7365
7367→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 7358, 7366
7368→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2
7369→→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7370→𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7368, 7369
7371→→𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜓↗→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7372→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7370, 7371
7373→→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7374→𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7372, 7373
7375→→𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7376→→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7374, 7375
7377→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7361, 7376
7378→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Subs [𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7379→→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7380→𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7378, 7379
7381→→𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2
7382→→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7380, 7381
7383→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7377, 7382
7384→→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2
7385→→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7383, 7384
7386→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7367, 7385
7387→→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7388→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7386, 7387
7389→→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7390→𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7388, 7389
7391→→𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→𝜒𝜑→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7392→→𝜑→𝜒𝜑→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7390, 7391
7393→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 13, 7392
7394→→𝜒→𝜑𝜒→¬¬𝜒→𝜒→𝜑𝜒Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗¬¬𝜒] into ax-1
7395→¬¬𝜒→𝜒→𝜑𝜒Modus ponens 1834, 7394
7396→→¬¬𝜒→𝜒→𝜑𝜒→→¬¬𝜒𝜒→¬¬𝜒→𝜑𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
7397→→¬¬𝜒𝜒→¬¬𝜒→𝜑𝜒Modus ponens 7395, 7396
7398→¬¬𝜒→𝜑𝜒Modus ponens 5153, 7397
7399→→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Subs [𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7400→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7393, 7399
7401→→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
7402→¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7400, 7401
7403→→¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2
7404→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7402, 7403
7405→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒Modus ponens 7398, 7404
7406→𝜑→¬¬𝜒𝜑Subs [𝜓↗¬¬𝜒] into ax-1
7407→→𝜑→¬¬𝜒𝜑→𝜑→𝜑→¬¬𝜒𝜑Subs [𝜑↗→𝜑→¬¬𝜒𝜑, 𝜓↗𝜑] into ax-1
7408→𝜑→𝜑→¬¬𝜒𝜑Modus ponens 7406, 7407
7409→→𝜑→𝜑→¬¬𝜒𝜑→→𝜑𝜑→𝜑→¬¬𝜒𝜑Subs [𝜓↗𝜑, 𝜒↗→¬¬𝜒𝜑] into ax-2
7410→→𝜑𝜑→𝜑→¬¬𝜒𝜑Modus ponens 7408, 7409
7411→→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7412→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7405, 7411
7413→→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7414→𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7412, 7413
7415→→𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7416→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7414, 7415
7417→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7406, 7416
7418→→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7419→𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7241, 7418
7420→→𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜓↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7421→→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7419, 7420
7422→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7417, 7421
7423→→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒, 𝜓↗𝜑] into ax-1
7424→𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Modus ponens 7247, 7423
7425→→𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Subs [𝜓↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-2
7426→→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Modus ponens 7424, 7425
7427→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒Modus ponens 7422, 7426
7428→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7429→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7430→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7428, 7429
7431→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜑¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7432→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7430, 7431
7433→→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒Subs [𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2
7434→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒Modus ponens 7427, 7433
7435→→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒Subs [𝜑↗→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7436→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒Modus ponens 7434, 7435
7437→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜑¬𝜒] into ax-2
7438→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒Modus ponens 7436, 7437
7439→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒Modus ponens 7428, 7438
7440→¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗¬→𝜑¬𝜒] into id
7441→→¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗→¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7442→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 7440, 7441
7443→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗¬→𝜑¬𝜒] into notnotr
7444→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7445→→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Subs [𝜑↗→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
7446→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Modus ponens 7444, 7445
7447→→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒] into ax-2
7448→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Modus ponens 7446, 7447
7449→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Modus ponens 7443, 7448
7450→→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2
7451→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Modus ponens 7442, 7450
7452→→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
7453→¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Modus ponens 7451, 7452
7454→→¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒] into ax-2
7455→→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒Modus ponens 7453, 7454
7456→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
7457→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7458→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7456, 7457
7459→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7460→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒Modus ponens 7458, 7459
7461→→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2
7462→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 7449, 7461
7463→→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7464→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 7462, 7463
7465→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒] into ax-2
7466→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 7464, 7465
7467→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 7456, 7466
7468→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒Subs [𝜑↗¬¬→𝜑¬𝜒, 𝜓↗→𝜑¬𝜒] into ax-3
7469→→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7470→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒Modus ponens 7468, 7469
7471→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→→𝜑¬𝜒¬¬→𝜑¬𝜒] into ax-2
7472→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒Modus ponens 7470, 7471
7473→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒Modus ponens 7467, 7472
7474→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗¬¬→𝜑¬𝜒] into ax-2
7475→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒Modus ponens 7473, 7474
7476→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒Modus ponens 7439, 7475
7477→→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜒] into ax-3
7478→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7476, 7477
7479→↔⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒¬→𝜑¬𝜒Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒] into biimp
7480→⋀𝜑𝜒¬→𝜑¬𝜒Modus ponens 6560, 7479
7481→→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜑𝜒] into ax-1
7482→⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7478, 7481
7483→→⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7484→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7482, 7483
7485→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒Modus ponens 7480, 7484
7486→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜑𝜒] into ax-1
7487→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
7488→→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓Modus ponens 7486, 7487
7489→→→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒→𝜑𝜓] into ax-2
7490→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓Modus ponens 7488, 7489
7491→→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2
7492→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒Modus ponens 7485, 7491
7493→→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7494→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒Modus ponens 7492, 7493
7495→→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜒] into ax-2
7496→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒Modus ponens 7494, 7495
7497→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒Modus ponens 7486, 7496pm3.45
7498↔→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.32
7499→↔→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓Subs [𝜑↗→𝜒↔𝜑𝜓, 𝜓↗↔⋀𝜒𝜑⋀𝜒𝜓] into biimp
7500→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓Modus ponens 7498, 7499
7501→→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓Subs [𝜑↗→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1
7502→↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓Modus ponens 7500, 7501
7503→→↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒↔𝜑𝜓, 𝜒↗↔⋀𝜒𝜑⋀𝜒𝜓] into ax-2
7504→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓Modus ponens 7502, 7503
7505→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓Modus ponens 2521, 7504anbi2
7506↔⋀𝜑𝜒⋀𝜒𝜑Subs [𝜓↗𝜒] into ancom
7507↔⋀𝜓𝜒⋀𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗𝜒] into ancom
7508→↔⋀𝜑𝜒⋀𝜒𝜑→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑Subs [𝜑↗↔⋀𝜑𝜒⋀𝜒𝜑, 𝜓↗↔𝜑𝜓] into ax-1
7509→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑Modus ponens 7506, 7508
7510↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜒𝜑] into pm5.74
7511→↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑] into biimp
7512→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑Modus ponens 7510, 7511
7513↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑Modus ponens 7509, 7512
7514↔→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜒𝜑, 𝜒↗⋀𝜒𝜓] into pm5.74
7515→↔→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓] into biimp
7516→→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7514, 7515
7517↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓Modus ponens anbi2, 7516
7518→↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp
7519→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7517, 7518
7520→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into biimp
7521→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑Modus ponens 7513, 7520
7522→→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into ax-1
7523→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7519, 7522
7524→→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑, 𝜒↗→↔𝜑𝜓⋀𝜒𝜓] into ax-2
7525→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7523, 7524
7526→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7521, 7525
7527→↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into bicom1
7528↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑Modus ponens 7517, 7527
7529→↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into biimp
7530→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑Modus ponens 7528, 7529
7531→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into bicom1
7532↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7513, 7531
7533→↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into biimp
7534→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7532, 7533
7535→→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into ax-1
7536→→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7534, 7535
7537→→→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑, 𝜒↗→↔𝜑𝜓⋀𝜑𝜒] into ax-2
7538→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7536, 7537
7539→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7530, 7538
7540→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into impbi
7541→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7526, 7540
7542↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7539, 7541
7543↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜒𝜓] into pm5.74
7544→↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓] into bicom1
7545↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓Modus ponens 7543, 7544
7546→↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓Subs [𝜑↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓] into biimp
7547→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓Modus ponens 7545, 7546
7548→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓Modus ponens 7542, 7547
7549→↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜒𝜓⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into bicom1
7550↔⋀𝜒𝜓⋀𝜓𝜒Modus ponens 7507, 7549
7551→↔⋀𝜒𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒Subs [𝜑↗↔⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
7552→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒Modus ponens 7550, 7551
7553→↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓] into biimp
7554→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7543, 7553
7555↔→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜓𝜒] into pm5.74
7556→↔→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒] into biimp
7557→→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒Modus ponens 7555, 7556
7558↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒Modus ponens 7552, 7557
7559→↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into biimp
7560→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒Modus ponens 7558, 7559
7561→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp
7562→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into ax-1
7563→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒Modus ponens 7560, 7562
7564→→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓, 𝜒↗→↔𝜑𝜓⋀𝜓𝜒] into ax-2
7565→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒Modus ponens 7563, 7564
7566→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒Modus ponens 7526, 7565
7567→↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into bicom1
7568↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7558, 7567
7569→↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp
7570→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓Modus ponens 7568, 7569
7571→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into bicom1
7572↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7542, 7571
7573→↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into biimp
7574→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into ax-1
7575→→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7539, 7574
7576→→→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓, 𝜒↗→↔𝜑𝜓⋀𝜑𝜒] into ax-2
7577→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7575, 7576
7578→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒Modus ponens 7570, 7577
7579→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into impbi
7580→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒Modus ponens 7566, 7579
7581↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒Modus ponens 7578, 7580
7582↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜓𝜒] into pm5.74
7583→↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒] into bicom1
7584↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒Modus ponens 7582, 7583
7585→↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒] into biimp
7586→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒Modus ponens 7584, 7585
7587→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒Modus ponens 7581, 7586anbi1
7588↔⋀𝜒𝜃⋀𝜃𝜒Subs [𝜑↗𝜒, 𝜓↗𝜃] into ancom
7589→↔⋀𝜒𝜃⋀𝜃𝜒→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒Subs [𝜑↗↔⋀𝜒𝜃⋀𝜃𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
7590→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒Modus ponens 7588, 7589
7591↔→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗⋀𝜃𝜒] into pm5.32
7592→↔→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒, 𝜓↗↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp
7593→→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7591, 7592
7594↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7590, 7593
7595→↔⋀𝜑𝜓⋀𝜓𝜑→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗⋀𝜃𝜒] into ax-1
7596→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑Modus ponens ancom, 7595
7597↔→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜃𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.32
7598→↔→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑Subs [𝜑↗→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp
7599→→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑Modus ponens 7597, 7598
7600↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑Modus ponens 7596, 7599
7601↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜃𝜒] into ancom
7602↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜓𝜑, 𝜓↗⋀𝜃𝜒] into ancom
7603→↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into bicom1
7604↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7602, 7603
7605→↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp
7606→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7604, 7605
7607→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp
7608→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑Modus ponens 7600, 7607
7609→→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into ax-1
7610→⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7606, 7609
7611→→⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2
7612→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7610, 7611
7613→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7608, 7612
7614→↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1
7615→↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp
7616→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑Modus ponens 7602, 7615
7617→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into bicom1
7618↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓Modus ponens 7600, 7617
7619→↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp
7620→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓Modus ponens 7618, 7619
7621→→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1
7622→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓Modus ponens 7620, 7621
7623→→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜃𝜒⋀𝜑𝜓] into ax-2
7624→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Modus ponens 7622, 7623
7625→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Modus ponens 7616, 7624
7626→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi
7627→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7613, 7626
7628↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7625, 7627
7629→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp
7630→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp
7631→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Modus ponens 7601, 7630
7632→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into ax-1
7633→⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7613, 7632
7634→→⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2
7635→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7633, 7634
7636→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7631, 7635
7637→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1
7638↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Modus ponens 7628, 7637
7639→↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp
7640→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into bicom1
7641↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7601, 7640
7642→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp
7643→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7641, 7642
7644→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1
7645→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7643, 7644
7646→→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜑𝜓⋀𝜃𝜒] into ax-2
7647→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7645, 7646
7648→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7625, 7647
7649→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi
7650→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7636, 7649
7651↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7648, 7650
7652→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp
7653→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp
7654→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7594, 7653
7655→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1
7656→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7636, 7655
7657→→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2
7658→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7656, 7657
7659→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7654, 7658
7660→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1
7661↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒Modus ponens 7651, 7660
7662→↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp
7663→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into bicom1
7664↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 7594, 7663
7665→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp
7666→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 7664, 7665
7667→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1
7668→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 7666, 7667
7669→→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2
7670→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 7668, 7669
7671→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 7648, 7670
7672→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi
7673→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7659, 7672
7674↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒Modus ponens 7671, 7673an2anr
7675→⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜃] into simpl
7676→⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜃] into simpr
7677→↔𝜑𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜒] into ax-1
7678→→↔𝜑𝜒→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7679→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒Modus ponens 7677, 7678
7680→→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗↔𝜑𝜒, 𝜒↗→𝜓↔𝜑𝜒] into ax-2
7681→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒Modus ponens 7679, 7680
7682→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒Modus ponens 7675, 7681
7683↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm5.32
7684→↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
7685→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 7683, 7684
7686→→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7687→⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 7685, 7686
7688→→⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
7689→→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 7687, 7688
7690→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 7682, 7689
7691→↔⋀𝜑𝜓⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7692→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑Modus ponens ancom, 7691
7693↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.74
7694→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp
7695→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Modus ponens 7693, 7694
7696↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Modus ponens 7692, 7695
7697↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜓𝜒] into pm5.74
7698→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7699→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7697, 7698
7700↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7690, 7699
7701→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7702→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7700, 7701
7703→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp
7704→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Modus ponens 7696, 7703
7705→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1
7706→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7702, 7705
7707→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into ax-2
7708→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7706, 7707
7709→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7704, 7708
7710→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1
7711↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Modus ponens 7700, 7710
7712→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp
7713→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑Modus ponens 7711, 7712
7714→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into bicom1
7715↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7696, 7714
7716→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp
7717→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7715, 7716
7718→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into ax-1
7719→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7717, 7718
7720→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2
7721→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7719, 7720
7722→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7713, 7721
7723→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into impbi
7724→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7709, 7723
7725↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7722, 7724
7726↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜒] into pm5.74
7727→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1
7728↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒Modus ponens 7726, 7727
7729→↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒] into biimp
7730→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒Modus ponens 7728, 7729
7731→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒Modus ponens 7725, 7730
7732→↔⋀𝜒𝜓⋀𝜓𝜒↔⋀𝜓𝜒⋀𝜒𝜓Subs [𝜑↗⋀𝜒𝜓, 𝜓↗⋀𝜓𝜒] into bicom1
7733→↔⋀𝜓𝜒⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓Subs [𝜑↗↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7734→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓Modus ponens 7507, 7733
7735→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7736→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7726, 7735
7737↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜒𝜓] into pm5.74
7738→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7739→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7737, 7738
7740↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7734, 7739
7741→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7742→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7740, 7741
7743→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7744→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1
7745→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7742, 7744
7746→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into ax-2
7747→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7745, 7746
7748→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7709, 7747
7749→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1
7750↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7740, 7749
7751→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7752→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒Modus ponens 7750, 7751
7753→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1
7754↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7725, 7753
7755→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp
7756→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into ax-1
7757→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7722, 7756
7758→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2
7759→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7757, 7758
7760→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7752, 7759
7761→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into impbi
7762→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7748, 7761
7763↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7760, 7762
7764↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜒𝜓] into pm5.74
7765→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1
7766↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓Modus ponens 7764, 7765
7767→↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓] into biimp
7768→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓Modus ponens 7766, 7767
7769→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓Modus ponens 7763, 7768
7770→↔𝜓𝜃→𝜒↔𝜓𝜃Subs [𝜑↗↔𝜓𝜃, 𝜓↗𝜒] into ax-1
7771→→↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃Subs [𝜑↗→↔𝜓𝜃→𝜒↔𝜓𝜃, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7772→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃Modus ponens 7770, 7771
7773→→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗↔𝜓𝜃, 𝜒↗→𝜒↔𝜓𝜃] into ax-2
7774→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃Modus ponens 7772, 7773
7775→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃Modus ponens 7676, 7774
7776↔→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃Subs [𝜑↗𝜒, 𝜒↗𝜃] into pm5.32
7777→↔→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃Subs [𝜑↗→𝜒↔𝜓𝜃, 𝜓↗↔⋀𝜒𝜓⋀𝜒𝜃] into biimp
7778→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃Modus ponens 7776, 7777
7779→→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃Subs [𝜑↗→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7780→⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃Modus ponens 7778, 7779
7781→→⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗→𝜒↔𝜓𝜃, 𝜒↗↔⋀𝜒𝜓⋀𝜒𝜃] into ax-2
7782→→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃Modus ponens 7780, 7781
7783→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃Modus ponens 7775, 7782
7784→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7785→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7764, 7784
7786↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜒𝜃] into pm5.74
7787→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into biimp
7788→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Modus ponens 7786, 7787
7789↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Modus ponens 7783, 7788
7790→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into biimp
7791→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Modus ponens 7789, 7790
7792→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7793→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1
7794→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Modus ponens 7791, 7793
7795→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into ax-2
7796→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Modus ponens 7794, 7795
7797→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Modus ponens 7748, 7796
7798→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into bicom1
7799↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7789, 7798
7800→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7801→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓Modus ponens 7799, 7800
7802→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1
7803↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7763, 7802
7804→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp
7805→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into ax-1
7806→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7760, 7805
7807→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2
7808→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7806, 7807
7809→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓Modus ponens 7801, 7808
7810→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into impbi
7811→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Modus ponens 7797, 7810
7812↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Modus ponens 7809, 7811
7813↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜒𝜃] into pm5.74
7814→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into bicom1
7815↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃Modus ponens 7813, 7814
7816→↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃] into biimp
7817→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃Modus ponens 7815, 7816
7818→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃Modus ponens 7812, 7817pm4.38
7819↔⋀𝜑𝜒⋀𝜑𝜒Subs [𝜑↗⋀𝜑𝜒] into biid
7820→↔⋀𝜑𝜒⋀𝜑𝜒→𝜓↔⋀𝜑𝜒⋀𝜑𝜒Subs [𝜑↗↔⋀𝜑𝜒⋀𝜑𝜒] into ax-1
7821→𝜓↔⋀𝜑𝜒⋀𝜑𝜒Modus ponens 7819, 7820
7822↔→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜑𝜒] into pm5.32
7823→↔→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗→𝜓↔⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒] into biimp
7824→→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7822, 7823
7825↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7821, 7824
7826↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗𝜓, 𝜓↗𝜑] into anass
7827→↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1
7828↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7826, 7827
7829→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp
7830→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7828, 7829
7831→↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp
7832→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7825, 7831
7833→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1
7834→⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7830, 7833
7835→→⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜓𝜑𝜒] into ax-2
7836→→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7834, 7835
7837→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into bicom1
7838→↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp
7839→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7826, 7838
7840→↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1
7841→→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into ax-1
7842→⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7832, 7841
7843→→⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2
7844→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7842, 7843
7845→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into impbi
7846→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7830, 7845
7847→↔⋀𝜓𝜑⋀𝜑𝜓→𝜒↔⋀𝜓𝜑⋀𝜑𝜓Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗𝜒] into ax-1
7848→𝜒↔⋀𝜓𝜑⋀𝜑𝜓Modus ponens 6162, 7847
7849↔→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.32
7850→↔→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓Subs [𝜑↗→𝜒↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓] into biimp
7851→→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓Modus ponens 7849, 7850
7852↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓Modus ponens 7848, 7851
7853↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜓𝜑, 𝜓↗𝜒] into ancom
7854↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ancom
7855→↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓] into bicom1
7856↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒Modus ponens 7854, 7855
7857→↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
7858→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒Modus ponens 7856, 7857
7859→↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓] into biimp
7860→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓Modus ponens 7852, 7859
7861→→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into ax-1
7862→⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒Modus ponens 7858, 7861
7863→→⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
7864→→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Modus ponens 7862, 7863
7865→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Modus ponens 7860, 7864
7866→↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
7867→↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓] into biimp
7868→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓Modus ponens 7854, 7867
7869→↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓] into bicom1
7870↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑Modus ponens 7852, 7869
7871→↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
7872→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑Modus ponens 7870, 7871
7873→→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑Subs [𝜑↗→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
7874→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑Modus ponens 7872, 7873
7875→→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓, 𝜒↗⋀𝜒⋀𝜓𝜑] into ax-2
7876→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑Modus ponens 7874, 7875
7877→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑Modus ponens 7868, 7876
7878→→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi
7879→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Modus ponens 7865, 7878
7880↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Modus ponens 7877, 7879
7881→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
7882→↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
7883→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑Modus ponens 7853, 7882
7884→→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into ax-1
7885→⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒Modus ponens 7865, 7884
7886→→⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
7887→→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7885, 7886
7888→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7883, 7887
7889→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
7890↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑Modus ponens 7880, 7889
7891→↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
7892→↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1
7893↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒Modus ponens 7853, 7892
7894→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp
7895→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒Modus ponens 7893, 7894
7896→→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
7897→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒Modus ponens 7895, 7896
7898→→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜓𝜑𝜒] into ax-2
7899→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7897, 7898
7900→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7877, 7899
7901→→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi
7902→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7888, 7901
7903↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7900, 7902
7904→↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
7905→→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1
7906→⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7888, 7905
7907→→⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
7908→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7906, 7907
7909→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7830, 7908
7910→↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
7911↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7903, 7910
7912→↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp
7913→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
7914→⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7839, 7913
7915→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2
7916→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7914, 7915
7917→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7900, 7916
7918→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi
7919→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7909, 7918
7920↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7917, 7919
7921→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
7922↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7920, 7921an21
7923→↔⋀𝜓𝜒⋀𝜒𝜓→𝜑↔⋀𝜓𝜒⋀𝜒𝜓Subs [𝜑↗↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗𝜑] into ax-1
7924→𝜑↔⋀𝜓𝜒⋀𝜒𝜓Modus ponens 7507, 7923
7925↔→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜒𝜓] into pm5.32
7926→↔→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓] into biimp
7927→→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓Modus ponens 7925, 7926
7928↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓Modus ponens 7924, 7927
7929↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓Subs [𝜓↗𝜒, 𝜒↗𝜓] into anass
7930→↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓] into bicom1
7931↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓Modus ponens 7929, 7930
7932→↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp
7933→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓Modus ponens 7931, 7932
7934→↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓] into biimp
7935→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓Modus ponens 7928, 7934
7936→→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓Subs [𝜑↗→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
7937→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓Modus ponens 7933, 7936
7938→→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓, 𝜒↗⋀⋀𝜑𝜒𝜓] into ax-2
7939→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7937, 7938
7940→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7935, 7939
7941→↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1
7942→↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓] into biimp
7943→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓Modus ponens 7929, 7942
7944→↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓] into bicom1
7945↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒Modus ponens 7928, 7944
7946→↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
7947→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒Modus ponens 7945, 7946
7948→→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into ax-1
7949→⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒Modus ponens 7947, 7948
7950→→⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
7951→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒Modus ponens 7949, 7950
7952→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒Modus ponens 7943, 7951
7953→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into impbi
7954→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7940, 7953
7955↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7952, 7954
7956↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜒] into ancom
7957→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1
7958↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒Modus ponens 7956, 7957
7959→↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp
7960→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒Modus ponens 7958, 7959
7961→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp
7962→→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒Subs [𝜑↗→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
7963→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒Modus ponens 7960, 7962
7964→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2
7965→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7963, 7964
7966→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7940, 7965
7967→↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1
7968→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp
7969→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7956, 7968
7970→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1
7971↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒Modus ponens 7955, 7970
7972→↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
7973→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1
7974→⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒Modus ponens 7952, 7973
7975→→⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
7976→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒Modus ponens 7974, 7975
7977→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒Modus ponens 7969, 7976
7978→→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒→→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into impbi
7979→→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7966, 7978
7980↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒Modus ponens 7977, 7979an12
7981→↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp
7982→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
7983→⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7969, 7982
7984→→⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜑𝜒𝜓] into ax-2
7985→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7983, 7984
7986→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7917, 7985
7987→↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1
7988→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
7989→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into ax-1
7990→⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒Modus ponens 7909, 7989
7991→→⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
7992→→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒Modus ponens 7990, 7991
7993→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒Modus ponens 7960, 7992
7994→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into impbi
7995→→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7986, 7994
7996↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓Modus ponens 7993, 7995an32
7997↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜑] into an21
7998→↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
7999↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7997, 7998
8000→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp
8001→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒Modus ponens 7999, 8000
8002→→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8003→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑Modus ponens 7883, 8002
8004→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜒⋀𝜓𝜑] into ax-2
8005→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑Modus ponens 8003, 8004
8006→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑Modus ponens 8001, 8005
8007→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into bicom1
8008→↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8009→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒Modus ponens 7997, 8008
8010→→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into ax-1
8011→⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒Modus ponens 8009, 8010
8012→→⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8013→→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8011, 8012
8014→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒Modus ponens 7895, 8013
8015→→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into impbi
8016→→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑Modus ponens 8006, 8015
8017↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑Modus ponens 8014, 8016an13
8018↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑Subs [𝜑↗𝜒, 𝜒↗𝜑] into anass
8019→↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1
8020↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑Modus ponens 8018, 8019
8021→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜒𝜓𝜑] into biimp
8022→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑Modus ponens 8020, 8021
8023→↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
8024→→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8025→⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑Modus ponens 8022, 8024
8026→→⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜒𝜓𝜑] into ax-2
8027→→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 8025, 8026
8028→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 8006, 8027
8029→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜒𝜓𝜑] into bicom1
8030→↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
8031→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑Modus ponens 8018, 8030
8032→↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1
8033↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒Modus ponens an13, 8032
8034→↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8035→→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into ax-1
8036→⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8014, 8035
8037→→⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8038→→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8036, 8037
8039→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8031, 8038
8040→→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into impbi
8041→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 8028, 8040
8042↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 8039, 8041
8043→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into biimp
8044→↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8045→→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
8046→⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 8028, 8045
8047→→⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜒𝜓𝜑] into ax-2
8048→→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 8046, 8047
8049→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 5253, 8048
8050→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into bicom1
8051↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8042, 8050
8052→↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8053→↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
8054↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens anass, 8053
8055→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
8056→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into ax-1
8057→⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 5573, 8056
8058→→⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
8059→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒Modus ponens 8057, 8058
8060→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒Modus ponens 8039, 8059
8061→→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into impbi
8062→→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 8049, 8061
8063↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑Modus ponens 8060, 8062an31
8064↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Subs [𝜒↗⋀𝜒𝜃] into anass
8065↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into an12
8066→↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃Subs [𝜑↗↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃, 𝜓↗𝜑] into ax-1
8067→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃Modus ponens 8065, 8066
8068↔→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Subs [𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗⋀𝜒⋀𝜓𝜃] into pm5.32
8069→↔→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Subs [𝜑↗→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃, 𝜓↗↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp
8070→→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Modus ponens 8068, 8069
8071↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Modus ponens 8067, 8070
8072↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Subs [𝜓↗𝜒, 𝜒↗⋀𝜓𝜃] into anass
8073→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into bicom1
8074↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8072, 8073
8075→↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp
8076→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8074, 8075
8077→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp
8078→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Modus ponens 8071, 8077
8079→→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1
8080→⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8076, 8079
8081→→⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-2
8082→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8080, 8081
8083→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8078, 8082
8084→↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1
8085→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp
8086→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃Modus ponens 8072, 8085
8087→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into bicom1
8088↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Modus ponens 8071, 8087
8089→↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp
8090→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Modus ponens 8088, 8089
8091→→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-1
8092→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Modus ponens 8090, 8091
8093→→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜒↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-2
8094→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Modus ponens 8092, 8093
8095→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Modus ponens 8086, 8094
8096→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into impbi
8097→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8083, 8096
8098↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8095, 8097
8099→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp
8100→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp
8101→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Modus ponens 8064, 8100
8102→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1
8103→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8083, 8102
8104→→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-2
8105→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8103, 8104
8106→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8101, 8105
8107→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1
8108↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Modus ponens 8098, 8107
8109→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp
8110→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into bicom1
8111↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 8064, 8110
8112→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp
8113→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 8111, 8112
8114→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-1
8115→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 8113, 8114
8116→→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2
8117→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 8115, 8116
8118→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 8095, 8117
8119→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into impbi
8120→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8106, 8119
8121↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8118, 8120an4
8122↔⋀𝜓𝜃⋀𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗𝜃] into ancom
8123→↔⋀𝜓𝜃⋀𝜃𝜓→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓Subs [𝜑↗↔⋀𝜓𝜃⋀𝜃𝜓, 𝜓↗⋀𝜑𝜒] into ax-1
8124→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓Modus ponens 8122, 8123
8125↔→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Subs [𝜑↗⋀𝜑𝜒, 𝜓↗⋀𝜓𝜃, 𝜒↗⋀𝜃𝜓] into pm5.32
8126→↔→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Subs [𝜑↗→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓, 𝜓↗↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓] into biimp
8127→→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Modus ponens 8125, 8126
8128↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Modus ponens 8124, 8127
8129→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into biimp
8130→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Modus ponens 8128, 8129
8131→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp
8132→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Subs [𝜑↗→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1
8133→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Modus ponens 8130, 8132
8134→→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜃𝜓] into ax-2
8135→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Modus ponens 8133, 8134
8136→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Modus ponens 8106, 8135
8137→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into bicom1
8138↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8128, 8137
8139→↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp
8140→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃Modus ponens 8138, 8139
8141→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1
8142↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens an4, 8141
8143→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp
8144→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into ax-1
8145→⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 8118, 8144
8146→→⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2
8147→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 8145, 8146
8148→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃Modus ponens 8140, 8147
8149→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into impbi
8150→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Modus ponens 8136, 8149
8151↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓Modus ponens 8148, 8150an42
8152↔⋀⋀𝜑𝜃⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜃Subs [𝜓↗𝜃, 𝜒↗𝜓, 𝜃↗𝜒] into an42
8153→↔⋀⋀𝜑𝜃⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜃⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into bicom1
8154↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒Modus ponens 8152, 8153an43
8155→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜃⋀𝜓𝜒] into biimp
8156→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒Modus ponens an43, 8155
8157→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃Subs [𝜑↗⋀𝜑𝜃, 𝜓↗⋀𝜓𝜒] into simpl
8158→→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃Subs [𝜑↗→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1
8159→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃Modus ponens 8157, 8158
8160→→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜃⋀𝜓𝜒, 𝜒↗⋀𝜑𝜃] into ax-2
8161→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃Modus ponens 8159, 8160
8162→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃Modus ponens 8156, 8161an3
8163↔→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑] into pm4.71
8164→↔→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑→→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑Subs [𝜑↗→⋀𝜑𝜓𝜑, 𝜓↗↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑] into biimp
8165→→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑Modus ponens 8163, 8164
8166↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑Modus ponens simpl, 8165
8167→↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑↔⋀⋀𝜑𝜓𝜑⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜑] into bicom1
8168↔⋀⋀𝜑𝜓𝜑⋀𝜑𝜓Modus ponens 8166, 8167anabs1
8169↔↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into bicom
8170→↔↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓Subs [𝜑↗↔𝜓⋀𝜑𝜓, 𝜓↗↔⋀𝜑𝜓𝜓] into biimp
8171→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓Modus ponens 8169, 8170
8172→→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓Subs [𝜑↗→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
8173→𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓Modus ponens 8171, 8172
8174→→𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→→𝜑↔𝜓⋀𝜑𝜓→𝜑↔⋀𝜑𝜓𝜓Subs [𝜓↗↔𝜓⋀𝜑𝜓, 𝜒↗↔⋀𝜑𝜓𝜓] into ax-2
8175→→𝜑↔𝜓⋀𝜑𝜓→𝜑↔⋀𝜑𝜓𝜓Modus ponens 8173, 8174
8176→𝜑↔⋀𝜑𝜓𝜓Modus ponens ibar, 8175
8177↔→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into pm5.32
8178→↔→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓→→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗→𝜑↔⋀𝜑𝜓𝜓, 𝜓↗↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp
8179→→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓Modus ponens 8177, 8178
8180↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓Modus ponens 8176, 8179anabs5
8181↔→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Subs [𝜑↗⋀𝜑𝜓] into pm4.71
8182→↔→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓] into biimp
8183→→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Modus ponens 8181, 8182
8184↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Modus ponens simpr, 8183
8185↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into ancom
8186→↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into bicom1
8187↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓Modus ponens 8185, 8186
8188→↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into biimp
8189→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓Modus ponens 8187, 8188
8190→↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into biimp
8191→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Modus ponens 8184, 8190
8192→→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓Subs [𝜑↗→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8193→⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓Modus ponens 8189, 8192
8194→→⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓, 𝜒↗⋀𝜓⋀𝜑𝜓] into ax-2
8195→→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓Modus ponens 8193, 8194
8196→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓Modus ponens 8191, 8195
8197→↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into bicom1
8198→↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into biimp
8199→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓Modus ponens 8185, 8198
8200→↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into bicom1
8201↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓Modus ponens 8184, 8200
8202→↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜑𝜓] into biimp
8203→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓Modus ponens 8201, 8202
8204→→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓Subs [𝜑↗→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into ax-1
8205→⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓Modus ponens 8203, 8204
8206→→⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓, 𝜒↗⋀𝜑𝜓] into ax-2
8207→→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓Modus ponens 8205, 8206
8208→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓Modus ponens 8199, 8207
8209→→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓→→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into impbi
8210→→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓Modus ponens 8196, 8209
8211↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓Modus ponens 8208, 8210
8212→↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓↔⋀𝜓⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into bicom1
8213↔⋀𝜓⋀𝜑𝜓⋀𝜑𝜓Modus ponens 8211, 8212anabs7
8214→↔⋀𝜑𝜑𝜑→⋀𝜓𝜒↔⋀𝜑𝜑𝜑Subs [𝜑↗↔⋀𝜑𝜑𝜑, 𝜓↗⋀𝜓𝜒] into ax-1
8215→⋀𝜓𝜒↔⋀𝜑𝜑𝜑Modus ponens anidm, 8214
8216↔→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜑𝜑, 𝜒↗𝜑] into pm5.32
8217→↔→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑Subs [𝜑↗→⋀𝜓𝜒↔⋀𝜑𝜑𝜑, 𝜓↗↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑] into biimp
8218→→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑Modus ponens 8216, 8217
8219↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑Modus ponens 8215, 8218
8220↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Subs [𝜑↗⋀𝜑𝜑, 𝜓↗⋀𝜓𝜒] into ancom
8221↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑Subs [𝜓↗⋀𝜓𝜒] into ancom
8222→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into bicom1
8223↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8221, 8222
8224→↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8225→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8223, 8224
8226→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp
8227→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑Modus ponens 8219, 8226
8228→→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into ax-1
8229→⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8225, 8228
8230→→⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8231→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8229, 8230
8232→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8227, 8231
8233→↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
8234→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp
8235→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑Modus ponens 8221, 8234
8236→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into bicom1
8237↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑Modus ponens 8219, 8236
8238→↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp
8239→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑Modus ponens 8237, 8238
8240→→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑Subs [𝜑↗→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8241→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑Modus ponens 8239, 8240
8242→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗⋀⋀𝜓𝜒⋀𝜑𝜑] into ax-2
8243→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Modus ponens 8241, 8242
8244→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Modus ponens 8235, 8243
8245→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi
8246→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8232, 8245
8247↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8244, 8246
8248→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8249→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp
8250→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Modus ponens 8220, 8249
8251→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into ax-1
8252→⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒Modus ponens 8232, 8251
8253→→⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8254→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 8252, 8253
8255→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 8250, 8254
8256→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
8257↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Modus ponens 8247, 8256
8258→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp
8259→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into bicom1
8260↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒Modus ponens 8220, 8259
8261→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp
8262→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒Modus ponens 8260, 8261
8263→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒Subs [𝜑↗→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8264→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒Modus ponens 8262, 8263
8265→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜒↗⋀⋀𝜑𝜑⋀𝜓𝜒] into ax-2
8266→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Modus ponens 8264, 8265
8267→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Modus ponens 8244, 8266
8268→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi
8269→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 8255, 8268
8270↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 8267, 8269
8271↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Subs [𝜓↗𝜑, 𝜒↗𝜓, 𝜃↗𝜒] into an4
8272→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
8273↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Modus ponens 8270, 8272
8274→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into biimp
8275→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Modus ponens 8271, 8274
8276→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp
8277→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8278→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Modus ponens 8275, 8277
8279→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓⋀𝜑𝜒] into ax-2
8280→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Modus ponens 8278, 8279
8281→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Modus ponens 8267, 8280
8282→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into bicom1
8283↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Modus ponens 8271, 8282
8284→↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp
8285→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒Modus ponens 8283, 8284
8286→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into bicom1
8287→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8288→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into ax-1
8289→⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒Modus ponens 8255, 8288
8290→→⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8291→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒Modus ponens 8289, 8290
8292→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒Modus ponens 8285, 8291
8293→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into impbi
8294→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Modus ponens 8281, 8293
8295↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒Modus ponens 8292, 8294anandi
8296↔⋀𝜒𝜒𝜒Subs [𝜑↗𝜒] into anidm
8297→↔⋀𝜒𝜒𝜒→⋀𝜑𝜓↔⋀𝜒𝜒𝜒Subs [𝜑↗↔⋀𝜒𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
8298→⋀𝜑𝜓↔⋀𝜒𝜒𝜒Modus ponens 8296, 8297
8299↔→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜒𝜒] into pm5.32
8300→↔→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓↔⋀𝜒𝜒𝜒, 𝜓↗↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒] into biimp
8301→→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Modus ponens 8299, 8300
8302↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Modus ponens 8298, 8301
8303↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Subs [𝜃↗𝜒] into an4
8304→↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
8305↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒Modus ponens 8302, 8304
8306→↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into biimp
8307→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Modus ponens 8303, 8306
8308→↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into biimp
8309→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒Modus ponens 8305, 8308
8310→→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
8311→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Modus ponens 8307, 8310
8312→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜒] into ax-2
8313→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Modus ponens 8311, 8312
8314→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Modus ponens 8309, 8313
8315→↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into bicom1
8316↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒Modus ponens 8303, 8315
8317→↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into biimp
8318→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒Modus ponens 8316, 8317
8319→↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into bicom1
8320→↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
8321→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Modus ponens 8302, 8320
8322→→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into ax-1
8323→⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒Modus ponens 8321, 8322
8324→→⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
8325→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 8323, 8324
8326→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒Modus ponens 8318, 8325
8327→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into impbi
8328→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Modus ponens 8314, 8327
8329↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒Modus ponens 8326, 8328anandir
8330↔⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒] into df-an
8331→¬¬→𝜓𝜒→𝜓𝜒Subs [𝜑↗→𝜓𝜒] into notnotr
8332→→𝜓𝜒→→𝜑𝜓→𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
8333→→→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒Subs [𝜑↗→→𝜓𝜒→→𝜑𝜓→𝜓𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1
8334→¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒Modus ponens 8332, 8333
8335→→¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒→→¬¬→𝜓𝜒→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓𝜒] into ax-2
8336→→¬¬→𝜓𝜒→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒Modus ponens 8334, 8335
8337→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒Modus ponens 8331, 8336
8338→→→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
8339→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens imim1, 8338
8340→→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1
8341→¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 8339, 8340
8342→→¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
8343→→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 8341, 8342
8344→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 8337, 8343
8345→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜓𝜒] into ax-1
8346→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
8347→→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓Modus ponens 8345, 8346
8348→→→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜓𝜒→𝜑𝜓] into ax-2
8349→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓Modus ponens 8347, 8348
8350→→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
8351→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒Modus ponens 8344, 8350
8352→→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
8353→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒Modus ponens 8351, 8352
8354→→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒→𝜑𝜓, 𝜒↗→¬¬→𝜓𝜒→𝜑𝜒] into ax-2
8355→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒Modus ponens 8353, 8354
8356→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒Modus ponens 8345, 8355
8357→→𝜑𝜒¬¬→𝜑𝜒Subs [𝜑↗→𝜑𝜒] into notnot
8358→→→𝜑𝜒¬¬→𝜑𝜒→¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒Subs [𝜑↗→→𝜑𝜒¬¬→𝜑𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1
8359→¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒Modus ponens 8357, 8358
8360→→¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜑𝜒, 𝜒↗¬¬→𝜑𝜒] into ax-2
8361→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒Modus ponens 8359, 8360
8362→→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒Subs [𝜑↗→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
8363→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒Modus ponens 8361, 8362
8364→→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒→𝜑𝜒, 𝜒↗→¬¬→𝜓𝜒¬¬→𝜑𝜒] into ax-2
8365→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒Modus ponens 8363, 8364
8366→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒Modus ponens 8356, 8365
8367→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒Subs [𝜑↗¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-3
8368→→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒→→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒Subs [𝜑↗→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
8369→→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒Modus ponens 8367, 8368
8370→→→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒→→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒¬¬→𝜑𝜒, 𝜒↗→¬→𝜑𝜒¬→𝜓𝜒] into ax-2
8371→→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒Modus ponens 8369, 8370
8372→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒Modus ponens 8366, 8371
8373→¬→𝜑𝜒¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒] into id
8374→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
8375→→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8376→¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒Modus ponens 8374, 8375
8377→→¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→→𝜑𝜓¬→𝜑𝜒] into ax-2
8378→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒Modus ponens 8376, 8377
8379→→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→𝜓𝜒] into ax-2
8380→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒Modus ponens 8372, 8379
8381→→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8382→¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒Modus ponens 8380, 8381
8383→→¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→→𝜑𝜓¬→𝜓𝜒] into ax-2
8384→→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒Modus ponens 8382, 8383
8385→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒Modus ponens 8374, 8384
8386→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒] into id
8387→→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8388→¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8386, 8387
8389→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒] into notnotr
8390→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8391→→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1
8392→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8390, 8391
8393→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8394→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8392, 8393
8395→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8389, 8394
8396→→¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8397→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8388, 8396
8398→→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1
8399→¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8397, 8398
8400→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8401→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8399, 8400
8402→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1
8403→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒Subs [𝜑↗→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8404→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒Modus ponens 8402, 8403
8405→→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒] into ax-2
8406→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒Modus ponens 8404, 8405
8407→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8408→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8395, 8407
8409→→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8410→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8408, 8409
8411→→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8412→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8410, 8411
8413→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8402, 8412
8414→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜓𝜒] into ax-3
8415→→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8416→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8414, 8415
8417→→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8418→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8416, 8417
8419→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8413, 8418
8420→→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8421→→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8419, 8420
8422→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8385, 8421
8423→→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-3
8424→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒Modus ponens 8422, 8423
8425→↔⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒] into biimp
8426→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒Modus ponens 8330, 8425
8427→→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒→⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒, 𝜓↗⋀→𝜑𝜓→𝜓𝜒] into ax-1
8428→⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒Modus ponens 8424, 8427
8429→→⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒→→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
8430→→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒Modus ponens 8428, 8429
8431→⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒Modus ponens 8426, 8430pm3.33
8432↔⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓] into df-an
8433→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
8434→¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens 63, 8433
8435→→¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2
8436→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens 8434, 8435
8437→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓Modus ponens 532, 8436
8438→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 68, 78
8439→→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1
8440→¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 8438, 8439
8441→→¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2
8442→→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 8440, 8441
8443→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒Modus ponens 8437, 8442
8444→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1
8445→→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒Subs [𝜑↗→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1
8446→→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒Modus ponens 8444, 8445
8447→→→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜓𝜒] into ax-2
8448→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒Modus ponens 8446, 8447
8449→→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
8450→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒Modus ponens 8443, 8449
8451→→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1
8452→→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒Modus ponens 8450, 8451
8453→→→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑𝜒] into ax-2
8454→→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒Modus ponens 8452, 8453
8455→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒Modus ponens 8444, 8454
8456→→→𝜑𝜒¬¬→𝜑𝜒→¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒Subs [𝜑↗→→𝜑𝜒¬¬→𝜑𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1
8457→¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒Modus ponens 8357, 8456
8458→→¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗¬¬→𝜑𝜒] into ax-2
8459→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒Modus ponens 8457, 8458
8460→→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1
8461→→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒Modus ponens 8459, 8460
8462→→→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑𝜒, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑𝜒] into ax-2
8463→→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒Modus ponens 8461, 8462
8464→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒Modus ponens 8455, 8463
8465→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-3
8466→→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓→→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-1
8467→→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓Modus ponens 8465, 8466
8468→→→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓→→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑𝜒, 𝜒↗→¬→𝜑𝜒¬→𝜑𝜓] into ax-2
8469→→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓Modus ponens 8467, 8468
8470→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓Modus ponens 8464, 8469
8471→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1
8472→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒Subs [𝜑↗→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8473→¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒Modus ponens 8471, 8472
8474→→¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→→𝜓𝜒¬→𝜑𝜒] into ax-2
8475→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒Modus ponens 8473, 8474
8476→→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗→𝜓𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→𝜑𝜓] into ax-2
8477→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓Modus ponens 8470, 8476
8478→→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8479→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓Modus ponens 8477, 8478
8480→→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜓𝜒¬→𝜑𝜒, 𝜒↗→→𝜓𝜒¬→𝜑𝜓] into ax-2
8481→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓Modus ponens 8479, 8480
8482→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓Modus ponens 8471, 8481
8483→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓] into id
8484→→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8485→¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8483, 8484
8486→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓] into notnotr
8487→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8488→→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1
8489→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8487, 8488
8490→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8491→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8489, 8490
8492→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8486, 8491
8493→→¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8494→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8485, 8493
8495→→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1
8496→¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8494, 8495
8497→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8498→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8496, 8497
8499→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1
8500→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8501→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒Modus ponens 8499, 8500
8502→→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒] into ax-2
8503→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒Modus ponens 8501, 8502
8504→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8505→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8492, 8504
8506→→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8507→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8505, 8506
8508→→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8509→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8507, 8508
8510→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8499, 8509
8511→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗→→𝜓𝜒¬→𝜑𝜓] into ax-3
8512→→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8513→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8511, 8512
8514→→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8515→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8513, 8514
8516→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8510, 8515
8517→→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜓𝜒¬→𝜑𝜓, 𝜒↗¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8518→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8516, 8517
8519→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8482, 8518
8520→→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜒, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-3
8521→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒Modus ponens 8519, 8520
8522→↔⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Subs [𝜑↗⋀→𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓] into biimp
8523→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓Modus ponens 8432, 8522
8524→→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒→⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒, 𝜓↗⋀→𝜓𝜒→𝜑𝜓] into ax-1
8525→⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒Modus ponens 8521, 8524
8526→→⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒→→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒Subs [𝜑↗⋀→𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
8527→→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒Modus ponens 8525, 8526
8528→⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒Modus ponens 8523, 8527pm3.34
8529→→𝜑→𝜒𝜑→→𝜑𝜒→𝜑𝜑Subs [𝜓↗𝜒, 𝜒↗𝜑] into ax-2
8530→→𝜑𝜒→𝜑𝜑Modus ponens 13, 8529
8531→→→𝜑𝜒→𝜑𝜑→¬¬𝜒→→𝜑𝜒→𝜑𝜑Subs [𝜑↗→→𝜑𝜒→𝜑𝜑, 𝜓↗¬¬𝜒] into ax-1
8532→¬¬𝜒→→𝜑𝜒→𝜑𝜑Modus ponens 8530, 8531
8533→→¬¬𝜒→→𝜑𝜒→𝜑𝜑→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑𝜑Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜑] into ax-2
8534→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑𝜑Modus ponens 8532, 8533
8535→¬¬𝜒→𝜑𝜑Modus ponens 7398, 8534
8536→→¬¬𝜒→𝜑𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2
8537→→¬¬𝜒𝜑→¬¬𝜒𝜑Modus ponens 8535, 8536
8538→→→¬¬𝜒𝜑→¬¬𝜒𝜑→𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒𝜑, 𝜓↗𝜑] into ax-1
8539→𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑Modus ponens 8537, 8538
8540→→𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒𝜑Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒𝜑] into ax-2
8541→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒𝜑Modus ponens 8539, 8540
8542→→𝜑¬¬𝜑→¬¬𝜒→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜒] into ax-1
8543→¬¬𝜒→𝜑¬¬𝜑Modus ponens notnot, 8542
8544→→¬¬𝜒→𝜑¬¬𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
8545→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑Modus ponens 8543, 8544
8546→→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑, 𝜓↗𝜑] into ax-1
8547→𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑Modus ponens 8545, 8546
8548→→𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒¬¬𝜑Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒¬¬𝜑] into ax-2
8549→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒¬¬𝜑Modus ponens 8547, 8548
8550→𝜑→¬¬𝜒¬¬𝜑Modus ponens 7406, 8549
8551→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜑] into ax-3
8552→→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒, 𝜓↗𝜑] into ax-1
8553→𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒Modus ponens 8551, 8552
8554→→𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→→𝜑→¬¬𝜒¬¬𝜑→𝜑→¬𝜑¬𝜒Subs [𝜓↗→¬¬𝜒¬¬𝜑, 𝜒↗→¬𝜑¬𝜒] into ax-2
8555→→𝜑→¬¬𝜒¬¬𝜑→𝜑→¬𝜑¬𝜒Modus ponens 8553, 8554
8556→𝜑→¬𝜑¬𝜒Modus ponens 8550, 8555
8557→→𝜑→¬𝜑¬𝜒→→𝜑¬𝜑→𝜑¬𝜒Subs [𝜓↗¬𝜑, 𝜒↗¬𝜒] into ax-2
8558→→𝜑¬𝜑→𝜑¬𝜒Modus ponens 8556, 8557
8559→→→𝜑¬𝜑→𝜑¬𝜒→¬𝜑→→𝜑¬𝜑→𝜑¬𝜒Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8560→¬𝜑→→𝜑¬𝜑→𝜑¬𝜒Modus ponens 8558, 8559
8561→→¬𝜑→→𝜑¬𝜑→𝜑¬𝜒→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜒] into ax-2
8562→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜒Modus ponens 8560, 8561
8563→¬𝜑→𝜑¬𝜒Modus ponens 414, 8562
8564→→¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗→¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8565→¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 7440, 8564
8566→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8567→→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Subs [𝜑↗→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
8568→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Modus ponens 8566, 8567
8569→→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→¬𝜑¬→𝜑¬𝜒] into ax-2
8570→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Modus ponens 8568, 8569
8571→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Modus ponens 7443, 8570
8572→→¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2
8573→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Modus ponens 8565, 8572
8574→→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Subs [𝜑↗→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
8575→¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Modus ponens 8573, 8574
8576→→¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗→¬𝜑¬→𝜑¬𝜒, 𝜒↗→¬𝜑¬→𝜑¬𝜒] into ax-2
8577→→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒Modus ponens 8575, 8576
8578→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
8579→→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1
8580→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑Modus ponens 8578, 8579
8581→→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜒¬𝜑] into ax-2
8582→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑Modus ponens 8580, 8581
8583→→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜒] into ax-2
8584→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 8571, 8583
8585→→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8586→¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 8584, 8585
8587→→¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜒¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒] into ax-2
8588→→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 8586, 8587
8589→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒Modus ponens 8578, 8588
8590→→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8591→¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒Modus ponens 7468, 8590
8592→→¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→→𝜑¬𝜒¬¬→𝜑¬𝜒] into ax-2
8593→→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒Modus ponens 8591, 8592
8594→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒Modus ponens 8589, 8593
8595→→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬𝜑→𝜑¬𝜒→¬𝜑¬¬→𝜑¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜒, 𝜒↗¬¬→𝜑¬𝜒] into ax-2
8596→→¬𝜑→𝜑¬𝜒→¬𝜑¬¬→𝜑¬𝜒Modus ponens 8594, 8595
8597→¬𝜑¬¬→𝜑¬𝜒Modus ponens 8563, 8596
8598→→¬𝜑¬¬→𝜑¬𝜒→¬→𝜑¬𝜒𝜑Subs [𝜓↗¬→𝜑¬𝜒] into ax-3
8599→¬→𝜑¬𝜒𝜑Modus ponens 8597, 8598
8600→→¬→𝜑¬𝜒𝜑→⋀𝜑𝜒→¬→𝜑¬𝜒𝜑Subs [𝜑↗→¬→𝜑¬𝜒𝜑, 𝜓↗⋀𝜑𝜒] into ax-1
8601→⋀𝜑𝜒→¬→𝜑¬𝜒𝜑Modus ponens 8599, 8600
8602→→⋀𝜑𝜒→¬→𝜑¬𝜒𝜑→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒𝜑Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗𝜑] into ax-2
8603→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒𝜑Modus ponens 8601, 8602
8604→⋀𝜑𝜒𝜑Modus ponens 7480, 8603
8605→↔¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒⋀𝜑𝜒Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜒] into biimp
8606→¬→𝜑¬𝜒⋀𝜑𝜒Modus ponens 6605, 8605
8607→→⋀𝜑𝜒𝜑→¬→𝜑¬𝜒→⋀𝜑𝜒𝜑Subs [𝜑↗→⋀𝜑𝜒𝜑, 𝜓↗¬→𝜑¬𝜒] into ax-1
8608→¬→𝜑¬𝜒→⋀𝜑𝜒𝜑Modus ponens 8604, 8607
8609→→¬→𝜑¬𝜒→⋀𝜑𝜒𝜑→→¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒𝜑Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜒, 𝜒↗𝜑] into ax-2
8610→→¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒𝜑Modus ponens 8608, 8609
8611→𝜑→𝜒¬→𝜑¬𝜒Subs [𝜓↗𝜒] into pm3.2im
8612→→¬→𝜑¬𝜒𝜑→𝜒→¬→𝜑¬𝜒𝜑Subs [𝜑↗→¬→𝜑¬𝜒𝜑, 𝜓↗𝜒] into ax-1
8613→𝜒→¬→𝜑¬𝜒𝜑Modus ponens 8599, 8612
8614→→𝜒→¬→𝜑¬𝜒𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗𝜑] into ax-2
8615→→𝜒¬→𝜑¬𝜒→𝜒𝜑Modus ponens 8613, 8614
8616→→→𝜒¬→𝜑¬𝜒→𝜒𝜑→𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑Subs [𝜑↗→→𝜒¬→𝜑¬𝜒→𝜒𝜑, 𝜓↗𝜑] into ax-1
8617→𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑Modus ponens 8615, 8616
8618→→𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑→→𝜑→𝜒¬→𝜑¬𝜒→𝜑→𝜒𝜑Subs [𝜓↗→𝜒¬→𝜑¬𝜒, 𝜒↗→𝜒𝜑] into ax-2
8619→→𝜑→𝜒¬→𝜑¬𝜒→𝜑→𝜒𝜑Modus ponens 8617, 8618
8620→→→𝜑𝜒→𝜑𝜑→𝜒→→𝜑𝜒→𝜑𝜑Subs [𝜑↗→→𝜑𝜒→𝜑𝜑, 𝜓↗𝜒] into ax-1
8621→𝜒→→𝜑𝜒→𝜑𝜑Modus ponens 8530, 8620
8622→→𝜒→→𝜑𝜒→𝜑𝜑→→𝜒→𝜑𝜒→𝜒→𝜑𝜑Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜑] into ax-2
8623→→𝜒→𝜑𝜒→𝜒→𝜑𝜑Modus ponens 8621, 8622
8624→𝜒→𝜑𝜑Modus ponens 1834, 8623
8625→→𝜑→𝜒𝜑→⋀𝜑𝜓→𝜑→𝜒𝜑Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8626→⋀𝜑𝜓→𝜑→𝜒𝜑Modus ponens 13, 8625
8627→→⋀𝜑𝜓→𝜑→𝜒𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜒𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2
8628→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜒𝜑Modus ponens 8626, 8627
8629→⋀𝜑𝜓→𝜒𝜑Modus ponens simpl, 8628
8630→→𝜒→𝜑𝜑→→𝜒𝜑→𝜒𝜑Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2
8631→→𝜒𝜑→𝜒𝜑Modus ponens 8624, 8630
8632→→→𝜒𝜑→𝜒𝜑→⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑Subs [𝜑↗→→𝜒𝜑→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8633→⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑Modus ponens 8631, 8632
8634→→⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑→→⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→𝜒𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒𝜑, 𝜒↗→𝜒𝜑] into ax-2
8635→→⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→𝜒𝜑Modus ponens 8633, 8634
8636→→𝜒→⋀𝜑𝜓𝜒→𝜒→𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
8637→𝜒→𝜒→⋀𝜑𝜓𝜒Modus ponens 5154, 8636
8638→→𝜒→𝜒→⋀𝜑𝜓𝜒→→𝜒𝜒→𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
8639→→𝜒𝜒→𝜒→⋀𝜑𝜓𝜒Modus ponens 8637, 8638
8640→→⋀𝜑𝜓→𝜒𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into ax-2
8641→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑Modus ponens 8629, 8640
8642→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑, 𝜓↗𝜒] into ax-1
8643→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑Modus ponens 8641, 8642
8644→→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜑Subs [𝜑↗𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
8645→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜑Modus ponens 8643, 8644
8646→𝜒→⋀𝜑𝜓𝜑Modus ponens 5154, 8645
8647→⋀𝜑𝜓→𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ax-1
8648→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓Subs [𝜑↗→⋀𝜑𝜓→𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8649→⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓Modus ponens 8647, 8648
8650→→⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜒⋀𝜑𝜓] into ax-2
8651→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓Modus ponens 8649, 8650
8652→→𝜒→⋀𝜑𝜓𝜑→→𝜒⋀𝜑𝜓→𝜒𝜑Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2
8653→→𝜒⋀𝜑𝜓→𝜒𝜑Modus ponens 8646, 8652
8654→→→𝜒⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑Subs [𝜑↗→→𝜒⋀𝜑𝜓→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8655→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑Modus ponens 8653, 8654
8656→→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒⋀𝜑𝜓, 𝜒↗→𝜒𝜑] into ax-2
8657→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜑Modus ponens 8655, 8656
8658→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑, 𝜓↗¬¬𝜒] into ax-1
8659→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑Modus ponens 8641, 8658
8660→→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜑Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
8661→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜑Modus ponens 8659, 8660
8662→¬¬𝜒→⋀𝜑𝜓𝜑Modus ponens 5159, 8661
8663→→¬¬𝜒→⋀𝜑𝜓𝜑→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2
8664→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑Modus ponens 8662, 8663
8665→→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8666→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑Modus ponens 8664, 8665
8667→→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒𝜑] into ax-2
8668→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜑Modus ponens 8666, 8667
8669→⋀𝜑𝜓→¬¬𝜒𝜑Modus ponens 5167, 8668
8670→→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8671→⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑Modus ponens 8545, 8670
8672→→⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→→⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→¬¬𝜒¬¬𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒¬¬𝜑] into ax-2
8673→→⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→¬¬𝜒¬¬𝜑Modus ponens 8671, 8672
8674→⋀𝜑𝜓→¬¬𝜒¬¬𝜑Modus ponens 8669, 8673
8675→→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
8676→⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒Modus ponens 8551, 8675
8677→→⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬𝜑, 𝜒↗→¬𝜑¬𝜒] into ax-2
8678→→⋀𝜑𝜓→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜒Modus ponens 8676, 8677
8679→⋀𝜑𝜓→¬𝜑¬𝜒Modus ponens 8674, 8678
8680→¬𝜑→⋀𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8681→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑Subs [𝜑↗→¬𝜑→⋀𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
8682→¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑Modus ponens 8680, 8681
8683→→¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜑] into ax-2
8684→→¬𝜑¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑Modus ponens 8682, 8683
8685→→⋀𝜑𝜓→¬𝜑¬𝜒→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜒] into ax-2
8686→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒Modus ponens 8679, 8685
8687→→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8688→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒Modus ponens 8686, 8687
8689→→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
8690→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜒Modus ponens 8688, 8689
8691→¬𝜑→⋀𝜑𝜓¬𝜒Modus ponens 8680, 8690
8692→→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8693→¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5208, 8692
8694→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8695→→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8696→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Modus ponens 8694, 8695
8697→→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜒] into ax-2
8698→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Modus ponens 8696, 8697
8699→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Modus ponens 5211, 8698
8700→→¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
8701→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Modus ponens 8693, 8700
8702→→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8703→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Modus ponens 8701, 8702
8704→→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜒] into ax-2
8705→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒Modus ponens 8703, 8704
8706→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8707→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1
8708→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑Modus ponens 8706, 8707
8709→→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑] into ax-2
8710→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑Modus ponens 8708, 8709
8711→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
8712→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 8699, 8711
8713→→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8714→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 8712, 8713
8715→→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
8716→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 8714, 8715
8717→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 8706, 8716
8718→→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8719→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 5236, 8718
8720→→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2
8721→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 8719, 8720
8722→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 8717, 8721
8723→→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2
8724→→¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑¬¬→⋀𝜑𝜓¬𝜒Modus ponens 8722, 8723
8725→¬𝜑¬¬→⋀𝜑𝜓¬𝜒Modus ponens 8691, 8724
8726→→¬𝜑¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒𝜑Subs [𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3
8727→¬→⋀𝜑𝜓¬𝜒𝜑Modus ponens 8725, 8726
8728→→¬→⋀𝜑𝜓¬𝜒𝜑→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
8729→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑Modus ponens 8727, 8728
8730→→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗𝜑] into ax-2
8731→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 8729, 8730
8732→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 5248, 8731simpll
8733→→𝜓→𝜒𝜓→→𝜓𝜒→𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into ax-2
8734→→𝜓𝜒→𝜓𝜓Modus ponens 5350, 8733
8735→→→𝜓𝜒→𝜓𝜓→¬¬𝜒→→𝜓𝜒→𝜓𝜓Subs [𝜑↗→→𝜓𝜒→𝜓𝜓, 𝜓↗¬¬𝜒] into ax-1
8736→¬¬𝜒→→𝜓𝜒→𝜓𝜓Modus ponens 8734, 8735
8737→→¬¬𝜒→→𝜓𝜒→𝜓𝜓→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜓Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜓] into ax-2
8738→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜓Modus ponens 8736, 8737
8739→¬¬𝜒→𝜓𝜓Modus ponens 5367, 8738
8740→→¬¬𝜒→𝜓𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓Subs [𝜑↗¬¬𝜒, 𝜒↗𝜓] into ax-2
8741→→¬¬𝜒𝜓→¬¬𝜒𝜓Modus ponens 8739, 8740
8742→→→¬¬𝜒𝜓→¬¬𝜒𝜓→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒𝜓] into ax-1
8743→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓Modus ponens 8741, 8742
8744→→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2
8745→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜓Modus ponens 8743, 8744
8746→→𝜓¬¬𝜓→¬¬𝜒→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜒] into ax-1
8747→¬¬𝜒→𝜓¬¬𝜓Modus ponens 448, 8746
8748→→¬¬𝜒→𝜓¬¬𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓Subs [𝜑↗¬¬𝜒, 𝜒↗¬¬𝜓] into ax-2
8749→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓Modus ponens 8747, 8748
8750→→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓] into ax-1
8751→𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓Modus ponens 8749, 8750
8752→→𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒¬¬𝜓Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒¬¬𝜓] into ax-2
8753→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒¬¬𝜓Modus ponens 8751, 8752
8754→𝜓→¬¬𝜒¬¬𝜓Modus ponens 5375, 8753
8755→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜓] into ax-3
8756→→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒] into ax-1
8757→𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒Modus ponens 8755, 8756
8758→→𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→→𝜓→¬¬𝜒¬¬𝜓→𝜓→¬𝜓¬𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬𝜓, 𝜒↗→¬𝜓¬𝜒] into ax-2
8759→→𝜓→¬¬𝜒¬¬𝜓→𝜓→¬𝜓¬𝜒Modus ponens 8757, 8758
8760→𝜓→¬𝜓¬𝜒Modus ponens 8754, 8759
8761→→𝜓→¬𝜓¬𝜒→→𝜓¬𝜓→𝜓¬𝜒Subs [𝜑↗𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜒] into ax-2
8762→→𝜓¬𝜓→𝜓¬𝜒Modus ponens 8760, 8761
8763→→→𝜓¬𝜓→𝜓¬𝜒→¬𝜓→→𝜓¬𝜓→𝜓¬𝜒Subs [𝜑↗→→𝜓¬𝜓→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8764→¬𝜓→→𝜓¬𝜓→𝜓¬𝜒Modus ponens 8762, 8763
8765→→¬𝜓→→𝜓¬𝜓→𝜓¬𝜒→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜓, 𝜒↗→𝜓¬𝜒] into ax-2
8766→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜒Modus ponens 8764, 8765
8767→¬𝜓→𝜓¬𝜒Modus ponens 5845, 8766
8768→→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8769→¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 5416, 8768
8770→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8771→→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Subs [𝜑↗→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
8772→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Modus ponens 8770, 8771
8773→→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬𝜓¬→𝜓¬𝜒] into ax-2
8774→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Modus ponens 8772, 8773
8775→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Modus ponens 5419, 8774
8776→→¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
8777→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Modus ponens 8769, 8776
8778→→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Subs [𝜑↗→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
8779→¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Modus ponens 8777, 8778
8780→→¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬𝜓¬→𝜓¬𝜒, 𝜒↗→¬𝜓¬→𝜓¬𝜒] into ax-2
8781→→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒Modus ponens 8779, 8780
8782→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
8783→→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
8784→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓Modus ponens 8782, 8783
8785→→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜒¬𝜓] into ax-2
8786→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓Modus ponens 8784, 8785
8787→→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬𝜓, 𝜒↗¬→𝜓¬𝜒] into ax-2
8788→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 8775, 8787
8789→→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8790→¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 8788, 8789
8791→→¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜒¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2
8792→→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 8790, 8791
8793→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 8782, 8792
8794→→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8795→¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 5444, 8794
8796→→¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2
8797→→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 8795, 8796
8798→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 8793, 8797
8799→→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜓→𝜓¬𝜒→¬𝜓¬¬→𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2
8800→→¬𝜓→𝜓¬𝜒→¬𝜓¬¬→𝜓¬𝜒Modus ponens 8798, 8799
8801→¬𝜓¬¬→𝜓¬𝜒Modus ponens 8767, 8800
8802→→¬𝜓¬¬→𝜓¬𝜒→¬→𝜓¬𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜓¬𝜒] into ax-3
8803→¬→𝜓¬𝜒𝜓Modus ponens 8801, 8802
8804→→¬→𝜓¬𝜒𝜓→⋀𝜓𝜒→¬→𝜓¬𝜒𝜓Subs [𝜑↗→¬→𝜓¬𝜒𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8805→⋀𝜓𝜒→¬→𝜓¬𝜒𝜓Modus ponens 8803, 8804
8806→→⋀𝜓𝜒→¬→𝜓¬𝜒𝜓→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗𝜓] into ax-2
8807→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜓Modus ponens 8805, 8806
8808→→⋀𝜓𝜒𝜓→¬→𝜓¬𝜒→⋀𝜓𝜒𝜓Subs [𝜑↗→⋀𝜓𝜒𝜓, 𝜓↗¬→𝜓¬𝜒] into ax-1
8809→¬→𝜓¬𝜒→⋀𝜓𝜒𝜓Modus ponens 6072, 8808
8810→→¬→𝜓¬𝜒→⋀𝜓𝜒𝜓→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒𝜓Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
8811→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒𝜓Modus ponens 8809, 8810
8812→→¬→𝜓¬𝜒𝜓→𝜒→¬→𝜓¬𝜒𝜓Subs [𝜑↗→¬→𝜓¬𝜒𝜓, 𝜓↗𝜒] into ax-1
8813→𝜒→¬→𝜓¬𝜒𝜓Modus ponens 8803, 8812
8814→→𝜒→¬→𝜓¬𝜒𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗𝜓] into ax-2
8815→→𝜒¬→𝜓¬𝜒→𝜒𝜓Modus ponens 8813, 8814
8816→→→𝜒¬→𝜓¬𝜒→𝜒𝜓→𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒𝜓] into ax-1
8817→𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓Modus ponens 8815, 8816
8818→→𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒𝜓] into ax-2
8819→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒𝜓Modus ponens 8817, 8818
8820→→→𝜓𝜒→𝜓𝜓→𝜒→→𝜓𝜒→𝜓𝜓Subs [𝜑↗→→𝜓𝜒→𝜓𝜓, 𝜓↗𝜒] into ax-1
8821→𝜒→→𝜓𝜒→𝜓𝜓Modus ponens 8734, 8820
8822→→𝜒→→𝜓𝜒→𝜓𝜓→→𝜒→𝜓𝜒→𝜒→𝜓𝜓Subs [𝜑↗𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜓] into ax-2
8823→→𝜒→𝜓𝜒→𝜒→𝜓𝜓Modus ponens 8821, 8822
8824→𝜒→𝜓𝜓Modus ponens 5362, 8823
8825→→𝜓→𝜒𝜓→⋀𝜑𝜓→𝜓→𝜒𝜓Subs [𝜑↗→𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8826→⋀𝜑𝜓→𝜓→𝜒𝜓Modus ponens 5350, 8825
8827→→⋀𝜑𝜓→𝜓→𝜒𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜒𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2
8828→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜒𝜓Modus ponens 8826, 8827
8829→⋀𝜑𝜓→𝜒𝜓Modus ponens simpr, 8828
8830→→𝜒→𝜓𝜓→→𝜒𝜓→𝜒𝜓Subs [𝜑↗𝜒, 𝜒↗𝜓] into ax-2
8831→→𝜒𝜓→𝜒𝜓Modus ponens 8824, 8830
8832→→→𝜒𝜓→𝜒𝜓→⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓Subs [𝜑↗→→𝜒𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8833→⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓Modus ponens 8831, 8832
8834→→⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓→→⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→𝜒𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜓] into ax-2
8835→→⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→𝜒𝜓Modus ponens 8833, 8834
8836→→⋀𝜑𝜓→𝜒𝜓→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into ax-2
8837→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓Modus ponens 8829, 8836
8838→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗𝜒] into ax-1
8839→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓Modus ponens 8837, 8838
8840→→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜓Subs [𝜑↗𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
8841→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜓Modus ponens 8839, 8840
8842→𝜒→⋀𝜑𝜓𝜓Modus ponens 5154, 8841
8843→→𝜒→⋀𝜑𝜓𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
8844→→𝜒⋀𝜑𝜓→𝜒𝜓Modus ponens 8842, 8843
8845→→→𝜒⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓Subs [𝜑↗→→𝜒⋀𝜑𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8846→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓Modus ponens 8844, 8845
8847→→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒⋀𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2
8848→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜓Modus ponens 8846, 8847
8849→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗¬¬𝜒] into ax-1
8850→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓Modus ponens 8837, 8849
8851→→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜓Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
8852→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜓Modus ponens 8850, 8851
8853→¬¬𝜒→⋀𝜑𝜓𝜓Modus ponens 5159, 8852
8854→→¬¬𝜒→⋀𝜑𝜓𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
8855→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓Modus ponens 8853, 8854
8856→→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8857→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓Modus ponens 8855, 8856
8858→→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2
8859→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜓Modus ponens 8857, 8858
8860→⋀𝜑𝜓→¬¬𝜒𝜓Modus ponens 5167, 8859
8861→→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8862→⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓Modus ponens 8749, 8861
8863→→⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→→⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→¬¬𝜒¬¬𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒¬¬𝜓] into ax-2
8864→→⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→¬¬𝜒¬¬𝜓Modus ponens 8862, 8863
8865→⋀𝜑𝜓→¬¬𝜒¬¬𝜓Modus ponens 8860, 8864
8866→→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
8867→⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒Modus ponens 8755, 8866
8868→→⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬𝜓, 𝜒↗→¬𝜓¬𝜒] into ax-2
8869→→⋀𝜑𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜒Modus ponens 8867, 8868
8870→⋀𝜑𝜓→¬𝜓¬𝜒Modus ponens 8865, 8869
8871→¬𝜓→⋀𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8872→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓Subs [𝜑↗→¬𝜓→⋀𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
8873→¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓Modus ponens 8871, 8872
8874→→¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜓] into ax-2
8875→→¬𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓Modus ponens 8873, 8874
8876→→⋀𝜑𝜓→¬𝜓¬𝜒→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜒] into ax-2
8877→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒Modus ponens 8870, 8876
8878→→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8879→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒Modus ponens 8877, 8878
8880→→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
8881→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜒Modus ponens 8879, 8880
8882→¬𝜓→⋀𝜑𝜓¬𝜒Modus ponens 8871, 8881
8883→→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8884→¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 5208, 8883
8885→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8886→→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8887→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Modus ponens 8885, 8886
8888→→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜒] into ax-2
8889→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Modus ponens 8887, 8888
8890→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Modus ponens 5211, 8889
8891→→¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
8892→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Modus ponens 8884, 8891
8893→→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8894→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Modus ponens 8892, 8893
8895→→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜒] into ax-2
8896→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒Modus ponens 8894, 8895
8897→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8898→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
8899→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓Modus ponens 8897, 8898
8900→→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓] into ax-2
8901→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓Modus ponens 8899, 8900
8902→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
8903→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 8890, 8902
8904→→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8905→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 8903, 8904
8906→→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
8907→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 8905, 8906
8908→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒Modus ponens 8897, 8907
8909→→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8910→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 5236, 8909
8911→→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2
8912→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 8910, 8911
8913→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒Modus ponens 8908, 8912
8914→→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓¬¬→⋀𝜑𝜓¬𝜒Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2
8915→→¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓¬¬→⋀𝜑𝜓¬𝜒Modus ponens 8913, 8914
8916→¬𝜓¬¬→⋀𝜑𝜓¬𝜒Modus ponens 8882, 8915
8917→→¬𝜓¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3
8918→¬→⋀𝜑𝜓¬𝜒𝜓Modus ponens 8916, 8917
8919→→¬→⋀𝜑𝜓¬𝜒𝜓→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
8920→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓Modus ponens 8918, 8919
8921→→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗𝜓] into ax-2
8922→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 8920, 8921
8923→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 5248, 8922simplr
8924→→𝜓→𝜑𝜓→⋀𝜓𝜒→𝜓→𝜑𝜓Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8925→⋀𝜓𝜒→𝜓→𝜑𝜓Modus ponens 208, 8924
8926→→⋀𝜓𝜒→𝜓→𝜑𝜓→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
8927→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜑𝜓Modus ponens 8925, 8926
8928→⋀𝜓𝜒→𝜑𝜓Modus ponens 6072, 8927
8929↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into df-an
8930→→𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→𝜑→⋀𝜓𝜒𝜑Subs [𝜑↗→𝜑→⋀𝜓𝜒𝜑, 𝜓↗¬¬𝜑] into ax-1
8931→¬¬𝜑→𝜑→⋀𝜓𝜒𝜑Modus ponens 5462, 8930
8932→→¬¬𝜑→𝜑→⋀𝜓𝜒𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓𝜒𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀𝜓𝜒𝜑] into ax-2
8933→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓𝜒𝜑Modus ponens 8931, 8932
8934→¬¬𝜑→⋀𝜓𝜒𝜑Modus ponens notnotr, 8933
8935→→⋀𝜓𝜒→𝜑𝜓→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
8936→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓Modus ponens 8928, 8935
8937→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜑] into ax-1
8938→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓Modus ponens 8936, 8937
8939→→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜓Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
8940→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜓Modus ponens 8938, 8939
8941→¬¬𝜑→⋀𝜓𝜒𝜓Modus ponens 8934, 8940
8942→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1
8943→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
8944→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒Modus ponens 8942, 8943
8945→→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→¬¬𝜑⋀𝜓𝜒] into ax-2
8946→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒Modus ponens 8944, 8945
8947→→¬¬𝜑→⋀𝜓𝜒𝜓→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
8948→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓Modus ponens 8941, 8947
8949→→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8950→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓Modus ponens 8948, 8949
8951→→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑𝜓] into ax-2
8952→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜓Modus ponens 8950, 8951
8953→⋀𝜓𝜒→¬¬𝜑𝜓Modus ponens 8942, 8952
8954→→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8955→⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓Modus ponens 488, 8954
8956→→⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→¬¬𝜑¬¬𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2
8957→→⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→¬¬𝜑¬¬𝜓Modus ponens 8955, 8956
8958→⋀𝜓𝜒→¬¬𝜑¬¬𝜓Modus ponens 8953, 8957
8959→→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-1
8960→⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑Modus ponens 494, 8959
8961→→⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→⋀𝜓𝜒→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜑Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
8962→→⋀𝜓𝜒→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜑Modus ponens 8960, 8961
8963→⋀𝜓𝜒→¬𝜓¬𝜑Modus ponens 8958, 8962
8964→¬𝜓→⋀𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8965→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓Subs [𝜑↗→¬𝜓→⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
8966→¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓Modus ponens 8964, 8965
8967→→¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜓] into ax-2
8968→→¬𝜓¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓Modus ponens 8966, 8967
8969→→⋀𝜓𝜒→¬𝜓¬𝜑→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2
8970→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑Modus ponens 8963, 8969
8971→→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
8972→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑Modus ponens 8970, 8971
8973→→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2
8974→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜑Modus ponens 8972, 8973
8975→¬𝜓→⋀𝜓𝜒¬𝜑Modus ponens 8964, 8974
8976→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑] into id
8977→→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
8978→¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 8976, 8977
8979→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑] into notnotr
8980→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
8981→→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
8982→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Modus ponens 8980, 8981
8983→→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜑] into ax-2
8984→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Modus ponens 8982, 8983
8985→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Modus ponens 8979, 8984
8986→→¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2
8987→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Modus ponens 8978, 8986
8988→→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
8989→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Modus ponens 8987, 8988
8990→→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜑] into ax-2
8991→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑Modus ponens 8989, 8990
8992→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
8993→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
8994→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓Modus ponens 8992, 8993
8995→→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓] into ax-2
8996→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓Modus ponens 8994, 8995
8997→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2
8998→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 8985, 8997
8999→→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
9000→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 8998, 8999
9001→→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑] into ax-2
9002→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 9000, 9001
9003→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 8992, 9002
9004→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜓𝜒¬𝜑] into ax-3
9005→→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
9006→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9004, 9005
9007→→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑] into ax-2
9008→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9006, 9007
9009→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9003, 9008
9010→→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓¬¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜑, 𝜒↗¬¬→⋀𝜓𝜒¬𝜑] into ax-2
9011→→¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9009, 9010
9012→¬𝜓¬¬→⋀𝜓𝜒¬𝜑Modus ponens 8975, 9011
9013→→¬𝜓¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-3
9014→¬→⋀𝜓𝜒¬𝜑𝜓Modus ponens 9012, 9013
9015→↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into biimp
9016→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 8929, 9015
9017→→¬→⋀𝜓𝜒¬𝜑𝜓→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜓, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-1
9018→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓Modus ponens 9014, 9017
9019→→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗𝜓] into ax-2
9020→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓Modus ponens 9018, 9019
9021→⋀⋀𝜓𝜒𝜑𝜓Modus ponens 9016, 9020
9022→↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into bicom1
9023↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑Modus ponens 8929, 9022
9024→↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp
9025→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑Modus ponens 9023, 9024
9026→→⋀⋀𝜓𝜒𝜑𝜓→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓Subs [𝜑↗→⋀⋀𝜓𝜒𝜑𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-1
9027→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓Modus ponens 9021, 9026
9028→→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗𝜓] into ax-2
9029→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓Modus ponens 9027, 9028
9030→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into pm3.2im
9031→→¬→⋀𝜓𝜒¬𝜑𝜓→𝜑→¬→⋀𝜓𝜒¬𝜑𝜓Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜓, 𝜓↗𝜑] into ax-1
9032→𝜑→¬→⋀𝜓𝜒¬𝜑𝜓Modus ponens 9014, 9031
9033→→𝜑→¬→⋀𝜓𝜒¬𝜑𝜓→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓Subs [𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗𝜓] into ax-2
9034→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓Modus ponens 9032, 9033
9035→→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓Subs [𝜑↗→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
9036→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓Modus ponens 9034, 9035
9037→→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→𝜑𝜓] into ax-2
9038→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜓Modus ponens 9036, 9037
9039→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
9040→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓Modus ponens 8936, 9039
9041→→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜓Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
9042→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜓Modus ponens 9040, 9041
9043→→→𝜑⋀𝜓𝜒→𝜑𝜓→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
9044→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 6076, 9043
9045→→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
9046→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜓Modus ponens 9044, 9045
9047→¬¬⋀𝜓𝜒→𝜑𝜓Modus ponens 5479, 9046
9048→→¬¬⋀𝜓𝜒→𝜑𝜓→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
9049→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓Modus ponens 9047, 9048
9050→→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
9051→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓Modus ponens 9049, 9050
9052→→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜓Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜓] into ax-2
9053→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜓Modus ponens 9051, 9052
9054→𝜑→¬¬⋀𝜓𝜒𝜓Modus ponens 5487, 9053
9055→→𝜓¬¬𝜓→¬¬⋀𝜓𝜒→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
9056→¬¬⋀𝜓𝜒→𝜓¬¬𝜓Modus ponens 448, 9055
9057→→¬¬⋀𝜓𝜒→𝜓¬¬𝜓→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜒↗¬¬𝜓] into ax-2
9058→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓Modus ponens 9056, 9057
9059→→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓, 𝜓↗𝜑] into ax-1
9060→𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓Modus ponens 9058, 9059
9061→→𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓→→𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→¬¬⋀𝜓𝜒¬¬𝜓Subs [𝜓↗→¬¬⋀𝜓𝜒𝜓, 𝜒↗→¬¬⋀𝜓𝜒¬¬𝜓] into ax-2
9062→→𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→¬¬⋀𝜓𝜒¬¬𝜓Modus ponens 9060, 9061
9063→𝜑→¬¬⋀𝜓𝜒¬¬𝜓Modus ponens 9054, 9062
9064→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-3
9065→→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
9066→𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒Modus ponens 9064, 9065
9067→→𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→¬𝜓¬⋀𝜓𝜒Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬𝜓, 𝜒↗→¬𝜓¬⋀𝜓𝜒] into ax-2
9068→→𝜑→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→¬𝜓¬⋀𝜓𝜒Modus ponens 9066, 9067
9069→𝜑→¬𝜓¬⋀𝜓𝜒Modus ponens 9063, 9068
9070→→𝜑→¬𝜓¬⋀𝜓𝜒→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒Subs [𝜓↗¬𝜓, 𝜒↗¬⋀𝜓𝜒] into ax-2
9071→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒Modus ponens 9069, 9070
9072→→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9073→¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒Modus ponens 9071, 9072
9074→→¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
9075→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬⋀𝜓𝜒Modus ponens 9073, 9074
9076→¬𝜓→𝜑¬⋀𝜓𝜒Modus ponens 609, 9075
9077→→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9078→¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5528, 9077
9079→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9080→→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9081→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Modus ponens 9079, 9080
9082→→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜓¬→𝜑¬⋀𝜓𝜒] into ax-2
9083→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Modus ponens 9081, 9082
9084→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Modus ponens 5531, 9083
9085→→¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9086→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Modus ponens 9078, 9085
9087→→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9088→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Modus ponens 9086, 9087
9089→→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜓¬→𝜑¬⋀𝜓𝜒] into ax-2
9090→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒Modus ponens 9088, 9089
9091→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9092→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
9093→¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓Modus ponens 9091, 9092
9094→→¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓] into ax-2
9095→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓Modus ponens 9093, 9094
9096→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9097→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9084, 9096
9098→→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9099→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9097, 9098
9100→→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
9101→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9099, 9100
9102→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9091, 9101
9103→→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9104→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 5556, 9103
9105→→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2
9106→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 9104, 9105
9107→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 9102, 9106
9108→→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2
9109→→¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓¬¬→𝜑¬⋀𝜓𝜒Modus ponens 9107, 9108
9110→¬𝜓¬¬→𝜑¬⋀𝜓𝜒Modus ponens 9076, 9109
9111→→¬𝜓¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3
9112→¬→𝜑¬⋀𝜓𝜒𝜓Modus ponens 9110, 9111
9113→→¬→𝜑¬⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9114→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓Modus ponens 9112, 9113
9115→→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
9116→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9114, 9115
9117→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 5568, 9116simprl
9118→⋀𝜑⋀𝜓𝜒𝜑Subs [𝜓↗⋀𝜓𝜒] into simpl
9119→→⋀𝜑𝜓𝜓→¬→𝜑¬𝜓→⋀𝜑𝜓𝜓Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-1
9120→¬→𝜑¬𝜓→⋀𝜑𝜓𝜓Modus ponens simpr, 9119
9121→→¬→𝜑¬𝜓→⋀𝜑𝜓𝜓→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
9122→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓𝜓Modus ponens 9120, 9121
9123→→¬→𝜑¬𝜓𝜓→𝜓→¬→𝜑¬𝜓𝜓Subs [𝜑↗→¬→𝜑¬𝜓𝜓] into ax-1
9124→𝜓→¬→𝜑¬𝜓𝜓Modus ponens simprim, 9123
9125→→𝜓→¬→𝜑¬𝜓𝜓→→𝜓¬→𝜑¬𝜓→𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜓] into ax-2
9126→→𝜓¬→𝜑¬𝜓→𝜓𝜓Modus ponens 9124, 9125
9127→→→𝜓¬→𝜑¬𝜓→𝜓𝜓→𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓𝜓, 𝜓↗𝜑] into ax-1
9128→𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓Modus ponens 9126, 9127
9129→→𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓𝜓Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓𝜓] into ax-2
9130→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓𝜓Modus ponens 9128, 9129
9131→→𝜓→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9132→⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓Modus ponens 208, 9131
9133→→⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓→→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
9134→→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 9132, 9133
9135→⋀𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens simprl, 9134
9136→→→𝜑𝜓→𝜑𝜓→⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9137→⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓Modus ponens 24, 9136
9138→→⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓→→⋀𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
9139→→⋀𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 9137, 9138
9140→𝜑→⋀𝜑⋀𝜓𝜒𝜑Subs [𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9141→→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑Subs [𝜑↗→𝜑→⋀𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1
9142→𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑Modus ponens 9140, 9141
9143→→𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜑] into ax-2
9144→→𝜑𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑Modus ponens 9142, 9143
9145→→⋀𝜑⋀𝜓𝜒→𝜑𝜓→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
9146→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9135, 9145
9147→→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓→𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
9148→𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9146, 9147
9149→→𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓→→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜓↗→⋀𝜑⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2
9150→→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9148, 9149
9151→𝜑→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9140, 9150
9152→→𝜑→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗→𝜑→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9153→⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9151, 9152
9154→→⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2
9155→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9153, 9154
9156→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9118, 9155
9157→→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
9158→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 9156, 9157
9159→→𝜒→𝜓𝜒→→𝜒𝜓→𝜒𝜒Subs [𝜑↗𝜒] into ax-2
9160→→𝜒𝜓→𝜒𝜒Modus ponens 5362, 9159
9161→→→𝜒𝜓→𝜒𝜒→¬¬𝜓→→𝜒𝜓→𝜒𝜒Subs [𝜑↗→→𝜒𝜓→𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1
9162→¬¬𝜓→→𝜒𝜓→𝜒𝜒Modus ponens 9160, 9161
9163→→¬¬𝜓→→𝜒𝜓→𝜒𝜒→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜒] into ax-2
9164→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒𝜒Modus ponens 9162, 9163
9165→¬¬𝜓→𝜒𝜒Modus ponens 7002, 9164
9166→→¬¬𝜓→𝜒𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒] into ax-2
9167→→¬¬𝜓𝜒→¬¬𝜓𝜒Modus ponens 9165, 9166
9168→→→¬¬𝜓𝜒→¬¬𝜓𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓𝜒, 𝜓↗𝜒] into ax-1
9169→𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒Modus ponens 9167, 9168
9170→→𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓𝜒] into ax-2
9171→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓𝜒Modus ponens 9169, 9170
9172→𝜒¬¬𝜒Subs [𝜑↗𝜒] into notnot
9173→→𝜒¬¬𝜒→¬¬𝜓→𝜒¬¬𝜒Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜓] into ax-1
9174→¬¬𝜓→𝜒¬¬𝜒Modus ponens 9172, 9173
9175→→¬¬𝜓→𝜒¬¬𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
9176→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒Modus ponens 9174, 9175
9177→→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒, 𝜓↗𝜒] into ax-1
9178→𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒Modus ponens 9176, 9177
9179→→𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓¬¬𝜒Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓¬¬𝜒] into ax-2
9180→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓¬¬𝜒Modus ponens 9178, 9179
9181→𝜒→¬¬𝜓¬¬𝜒Modus ponens 7010, 9180
9182→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜒] into ax-3
9183→→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓, 𝜓↗𝜒] into ax-1
9184→𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓Modus ponens 9182, 9183
9185→→𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→→𝜒→¬¬𝜓¬¬𝜒→𝜒→¬𝜒¬𝜓Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓¬¬𝜒, 𝜒↗→¬𝜒¬𝜓] into ax-2
9186→→𝜒→¬¬𝜓¬¬𝜒→𝜒→¬𝜒¬𝜓Modus ponens 9184, 9185
9187→𝜒→¬𝜒¬𝜓Modus ponens 9181, 9186
9188→¬𝜒¬𝜒Subs [𝜑↗¬𝜒] into id
9189→¬𝜒→𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗𝜒] into ax-1
9190→→¬𝜒→𝜒¬𝜒→¬𝜒→¬𝜒→𝜒¬𝜒Subs [𝜑↗→¬𝜒→𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
9191→¬𝜒→¬𝜒→𝜒¬𝜒Modus ponens 9189, 9190
9192→→¬𝜒→¬𝜒→𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜒¬𝜒] into ax-2
9193→→¬𝜒¬𝜒→¬𝜒→𝜒¬𝜒Modus ponens 9191, 9192
9194→→𝜒→¬𝜒¬𝜓→→𝜒¬𝜒→𝜒¬𝜓Subs [𝜑↗𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜓] into ax-2
9195→→𝜒¬𝜒→𝜒¬𝜓Modus ponens 9187, 9194
9196→→→𝜒¬𝜒→𝜒¬𝜓→¬𝜒→→𝜒¬𝜒→𝜒¬𝜓Subs [𝜑↗→→𝜒¬𝜒→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9197→¬𝜒→→𝜒¬𝜒→𝜒¬𝜓Modus ponens 9195, 9196
9198→→¬𝜒→→𝜒¬𝜒→𝜒¬𝜓→→¬𝜒→𝜒¬𝜒→¬𝜒→𝜒¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗→𝜒¬𝜒, 𝜒↗→𝜒¬𝜓] into ax-2
9199→→¬𝜒→𝜒¬𝜒→¬𝜒→𝜒¬𝜓Modus ponens 9197, 9198
9200→¬𝜒→𝜒¬𝜓Modus ponens 9189, 9199
9201→→¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗→¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9202→¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 7051, 9201
9203→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9204→→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Subs [𝜑↗→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
9205→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Modus ponens 9203, 9204
9206→→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→¬𝜒¬→𝜒¬𝜓] into ax-2
9207→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Modus ponens 9205, 9206
9208→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Modus ponens 7054, 9207
9209→→¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜒¬𝜓, 𝜒↗¬→𝜒¬𝜓] into ax-2
9210→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Modus ponens 9202, 9209
9211→→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Subs [𝜑↗→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
9212→¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Modus ponens 9210, 9211
9213→→¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗→¬𝜒¬→𝜒¬𝜓, 𝜒↗→¬𝜒¬→𝜒¬𝜓] into ax-2
9214→→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓Modus ponens 9212, 9213
9215→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
9216→→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9217→¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒Modus ponens 9215, 9216
9218→→¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬𝜒] into ax-2
9219→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒Modus ponens 9217, 9218
9220→→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬𝜒, 𝜒↗¬→𝜒¬𝜓] into ax-2
9221→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 9208, 9220
9222→→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9223→¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 9221, 9222
9224→→¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓] into ax-2
9225→→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 9223, 9224
9226→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓Modus ponens 9215, 9225
9227→→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9228→¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓Modus ponens 7079, 9227
9229→→¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜒↗→→𝜒¬𝜓¬¬→𝜒¬𝜓] into ax-2
9230→→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓Modus ponens 9228, 9229
9231→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓Modus ponens 9226, 9230
9232→→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬𝜒→𝜒¬𝜓→¬𝜒¬¬→𝜒¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗→𝜒¬𝜓, 𝜒↗¬¬→𝜒¬𝜓] into ax-2
9233→→¬𝜒→𝜒¬𝜓→¬𝜒¬¬→𝜒¬𝜓Modus ponens 9231, 9232
9234→¬𝜒¬¬→𝜒¬𝜓Modus ponens 9200, 9233
9235→→¬𝜒¬¬→𝜒¬𝜓→¬→𝜒¬𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-3
9236→¬→𝜒¬𝜓𝜒Modus ponens 9234, 9235
9237→→¬→𝜒¬𝜓𝜒→⋀𝜒𝜓→¬→𝜒¬𝜓𝜒Subs [𝜑↗→¬→𝜒¬𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1
9238→⋀𝜒𝜓→¬→𝜒¬𝜓𝜒Modus ponens 9236, 9237
9239→→⋀𝜒𝜓→¬→𝜒¬𝜓𝜒→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓𝜒Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into ax-2
9240→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓𝜒Modus ponens 9238, 9239
9241→⋀𝜒𝜓𝜒Modus ponens 7091, 9240
9242→→⋀𝜒𝜓𝜒→¬→𝜒¬𝜓→⋀𝜒𝜓𝜒Subs [𝜑↗→⋀𝜒𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-1
9243→¬→𝜒¬𝜓→⋀𝜒𝜓𝜒Modus ponens 9241, 9242
9244→→¬→𝜒¬𝜓→⋀𝜒𝜓𝜒→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓𝜒Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓] into ax-2
9245→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓𝜒Modus ponens 9243, 9244
9246→→¬→𝜒¬𝜓𝜒→𝜓→¬→𝜒¬𝜓𝜒Subs [𝜑↗→¬→𝜒¬𝜓𝜒] into ax-1
9247→𝜓→¬→𝜒¬𝜓𝜒Modus ponens 9236, 9246
9248→→𝜓→¬→𝜒¬𝜓𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗¬→𝜒¬𝜓] into ax-2
9249→→𝜓¬→𝜒¬𝜓→𝜓𝜒Modus ponens 9247, 9248
9250→→→𝜓¬→𝜒¬𝜓→𝜓𝜒→𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒Subs [𝜑↗→→𝜓¬→𝜒¬𝜓→𝜓𝜒, 𝜓↗𝜒] into ax-1
9251→𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒Modus ponens 9249, 9250
9252→→𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜓¬→𝜒¬𝜓, 𝜒↗→𝜓𝜒] into ax-2
9253→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓𝜒Modus ponens 9251, 9252
9254→→→𝜒𝜓→𝜒𝜒→𝜓→→𝜒𝜓→𝜒𝜒Subs [𝜑↗→→𝜒𝜓→𝜒𝜒] into ax-1
9255→𝜓→→𝜒𝜓→𝜒𝜒Modus ponens 9160, 9254
9256→→𝜓→→𝜒𝜓→𝜒𝜒→→𝜓→𝜒𝜓→𝜓→𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜒] into ax-2
9257→→𝜓→𝜒𝜓→𝜓→𝜒𝜒Modus ponens 9255, 9256
9258→→→𝜓𝜒→𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓𝜒Subs [𝜑↗→→𝜓𝜒→𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
9259→¬¬𝜒→→𝜓𝜒→𝜓𝜒Modus ponens 867, 9258
9260→→¬¬𝜒→→𝜓𝜒→𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
9261→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜒Modus ponens 9259, 9260
9262→→¬¬𝜒→𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒𝜒Subs [𝜑↗¬¬𝜒] into ax-2
9263→→¬¬𝜒𝜓→¬¬𝜒𝜒Modus ponens 5367, 9262
9264→→→¬¬𝜒𝜓→¬¬𝜒𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒𝜒] into ax-1
9265→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒Modus ponens 9263, 9264
9266→→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒𝜒] into ax-2
9267→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜒Modus ponens 9265, 9266
9268→𝜓→¬¬𝜒𝜒Modus ponens 5375, 9267
9269→→𝜒¬¬𝜒→¬¬𝜒→𝜒¬¬𝜒Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜒] into ax-1
9270→¬¬𝜒→𝜒¬¬𝜒Modus ponens 9172, 9269
9271→→¬¬𝜒→𝜒¬¬𝜒→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
9272→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒Modus ponens 9270, 9271
9273→→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒→𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒Subs [𝜑↗→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒] into ax-1
9274→𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒Modus ponens 9272, 9273
9275→→𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒→→𝜓→¬¬𝜒𝜒→𝜓→¬¬𝜒¬¬𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜒, 𝜒↗→¬¬𝜒¬¬𝜒] into ax-2
9276→→𝜓→¬¬𝜒𝜒→𝜓→¬¬𝜒¬¬𝜒Modus ponens 9274, 9275
9277→𝜓→¬¬𝜒¬¬𝜒Modus ponens 9268, 9276
9278→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒] into ax-3
9279→→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒→𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒] into ax-1
9280→𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒Modus ponens 9278, 9279
9281→→𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒→→𝜓→¬¬𝜒¬¬𝜒→𝜓→¬𝜒¬𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬𝜒, 𝜒↗→¬𝜒¬𝜒] into ax-2
9282→→𝜓→¬¬𝜒¬¬𝜒→𝜓→¬𝜒¬𝜒Modus ponens 9280, 9281
9283→𝜓→¬𝜒¬𝜒Modus ponens 9277, 9282
9284→¬𝜒→𝜓¬𝜒Subs [𝜑↗¬𝜒] into ax-1
9285→→¬𝜒→𝜓¬𝜒→¬𝜒→¬𝜒→𝜓¬𝜒Subs [𝜑↗→¬𝜒→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9286→¬𝜒→¬𝜒→𝜓¬𝜒Modus ponens 9284, 9285
9287→→¬𝜒→¬𝜒→𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜓¬𝜒] into ax-2
9288→→¬𝜒¬𝜒→¬𝜒→𝜓¬𝜒Modus ponens 9286, 9287
9289→→𝜓→¬𝜒¬𝜒→→𝜓¬𝜒→𝜓¬𝜒Subs [𝜑↗𝜓, 𝜓↗¬𝜒, 𝜒↗¬𝜒] into ax-2
9290→→𝜓¬𝜒→𝜓¬𝜒Modus ponens 9283, 9289
9291→→→𝜓¬𝜒→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒→𝜓¬𝜒Subs [𝜑↗→→𝜓¬𝜒→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9292→¬𝜒→→𝜓¬𝜒→𝜓¬𝜒Modus ponens 9290, 9291
9293→→¬𝜒→→𝜓¬𝜒→𝜓¬𝜒→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗→𝜓¬𝜒] into ax-2
9294→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬𝜒Modus ponens 9292, 9293
9295→→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9296→¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 5416, 9295
9297→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9298→→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
9299→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Modus ponens 9297, 9298
9300→→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬𝜒¬→𝜓¬𝜒] into ax-2
9301→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Modus ponens 9299, 9300
9302→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Modus ponens 5419, 9301
9303→→¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
9304→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Modus ponens 9296, 9303
9305→→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
9306→¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Modus ponens 9304, 9305
9307→→¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬𝜒¬→𝜓¬𝜒, 𝜒↗→¬𝜒¬→𝜓¬𝜒] into ax-2
9308→→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒Modus ponens 9306, 9307
9309→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
9310→→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
9311→¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒Modus ponens 9309, 9310
9312→→¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬𝜒] into ax-2
9313→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒Modus ponens 9311, 9312
9314→→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
9315→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 9302, 9314
9316→→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9317→¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 9315, 9316
9318→→¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2
9319→→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 9317, 9318
9320→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒Modus ponens 9309, 9319
9321→→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9322→¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 5444, 9321
9323→→¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2
9324→→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 9322, 9323
9325→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒Modus ponens 9320, 9324
9326→→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜒→𝜓¬𝜒→¬𝜒¬¬→𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2
9327→→¬𝜒→𝜓¬𝜒→¬𝜒¬¬→𝜓¬𝜒Modus ponens 9325, 9326
9328→¬𝜒¬¬→𝜓¬𝜒Modus ponens 9284, 9327
9329→→¬𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒𝜒Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3
9330→¬→𝜓¬𝜒𝜒Modus ponens 9328, 9329
9331→→¬→𝜓¬𝜒𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒𝜒Subs [𝜑↗→¬→𝜓¬𝜒𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9332→⋀𝜓𝜒→¬→𝜓¬𝜒𝜒Modus ponens 9330, 9331
9333→→⋀𝜓𝜒→¬→𝜓¬𝜒𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-2
9334→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜒Modus ponens 9332, 9333
9335→→𝜒→𝜑𝜒→⋀𝜓𝜒→𝜒→𝜑𝜒Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9336→⋀𝜓𝜒→𝜒→𝜑𝜒Modus ponens 1834, 9335
9337→→⋀𝜓𝜒→𝜒→𝜑𝜒→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
9338→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜑𝜒Modus ponens 9336, 9337
9339→⋀𝜓𝜒→𝜑𝜒Modus ponens 6077, 9338
9340→→⋀𝜓𝜒→𝜑𝜒→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into ax-2
9341→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒Modus ponens 9339, 9340
9342→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜑] into ax-1
9343→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒Modus ponens 9341, 9342
9344→→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜒Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
9345→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜒Modus ponens 9343, 9344
9346→¬¬𝜑→⋀𝜓𝜒𝜒Modus ponens 8934, 9345
9347→→¬¬𝜑→⋀𝜓𝜒𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-2
9348→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒Modus ponens 9346, 9347
9349→→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9350→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒Modus ponens 9348, 9349
9351→→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑𝜒] into ax-2
9352→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜒Modus ponens 9350, 9351
9353→⋀𝜓𝜒→¬¬𝜑𝜒Modus ponens 8942, 9352
9354→→𝜒¬¬𝜒→¬¬𝜑→𝜒¬¬𝜒Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜑] into ax-1
9355→¬¬𝜑→𝜒¬¬𝜒Modus ponens 9172, 9354
9356→→¬¬𝜑→𝜒¬¬𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒Subs [𝜑↗¬¬𝜑, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
9357→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒Modus ponens 9355, 9356
9358→→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒Subs [𝜑↗→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9359→⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒Modus ponens 9357, 9358
9360→→⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→→⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→¬¬𝜑¬¬𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑𝜒, 𝜒↗→¬¬𝜑¬¬𝜒] into ax-2
9361→→⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→¬¬𝜑¬¬𝜒Modus ponens 9359, 9360
9362→⋀𝜓𝜒→¬¬𝜑¬¬𝜒Modus ponens 9353, 9361
9363→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜒] into ax-3
9364→→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑Subs [𝜑↗→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-1
9365→⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑Modus ponens 9363, 9364
9366→→⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→→⋀𝜓𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜑Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑¬¬𝜒, 𝜒↗→¬𝜒¬𝜑] into ax-2
9367→→⋀𝜓𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜑Modus ponens 9365, 9366
9368→⋀𝜓𝜒→¬𝜒¬𝜑Modus ponens 9362, 9367
9369→¬𝜒→⋀𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9370→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒Subs [𝜑↗→¬𝜒→⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
9371→¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒Modus ponens 9369, 9370
9372→→¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜒] into ax-2
9373→→¬𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒Modus ponens 9371, 9372
9374→→⋀𝜓𝜒→¬𝜒¬𝜑→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜑] into ax-2
9375→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑Modus ponens 9368, 9374
9376→→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9377→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑Modus ponens 9375, 9376
9378→→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2
9379→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜑Modus ponens 9377, 9378
9380→¬𝜒→⋀𝜓𝜒¬𝜑Modus ponens 9369, 9379
9381→→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9382→¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 8976, 9381
9383→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9384→→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
9385→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Modus ponens 9383, 9384
9386→→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜑] into ax-2
9387→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Modus ponens 9385, 9386
9388→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Modus ponens 8979, 9387
9389→→¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2
9390→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Modus ponens 9382, 9389
9391→→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
9392→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Modus ponens 9390, 9391
9393→→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜑] into ax-2
9394→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑Modus ponens 9392, 9393
9395→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
9396→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1
9397→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒Modus ponens 9395, 9396
9398→→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒] into ax-2
9399→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒Modus ponens 9397, 9398
9400→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2
9401→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 9388, 9400
9402→→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9403→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 9401, 9402
9404→→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑] into ax-2
9405→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 9403, 9404
9406→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑Modus ponens 9395, 9405
9407→→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9408→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9004, 9407
9409→→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑] into ax-2
9410→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9408, 9409
9411→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9406, 9410
9412→→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒¬¬→⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑, 𝜒↗¬¬→⋀𝜓𝜒¬𝜑] into ax-2
9413→→¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9411, 9412
9414→¬𝜒¬¬→⋀𝜓𝜒¬𝜑Modus ponens 9380, 9413
9415→→¬𝜒¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-3
9416→¬→⋀𝜓𝜒¬𝜑𝜒Modus ponens 9414, 9415
9417→→¬→⋀𝜓𝜒¬𝜑𝜒→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-1
9418→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒Modus ponens 9416, 9417
9419→→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-2
9420→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒Modus ponens 9418, 9419
9421→⋀⋀𝜓𝜒𝜑𝜒Modus ponens 9016, 9420
9422→→⋀⋀𝜓𝜒𝜑𝜒→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒Subs [𝜑↗→⋀⋀𝜓𝜒𝜑𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-1
9423→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒Modus ponens 9421, 9422
9424→→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-2
9425→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒Modus ponens 9423, 9424
9426→→¬→⋀𝜓𝜒¬𝜑𝜒→𝜑→¬→⋀𝜓𝜒¬𝜑𝜒Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜒, 𝜓↗𝜑] into ax-1
9427→𝜑→¬→⋀𝜓𝜒¬𝜑𝜒Modus ponens 9416, 9426
9428→→𝜑→¬→⋀𝜓𝜒¬𝜑𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒Subs [𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-2
9429→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒Modus ponens 9427, 9428
9430→→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒Subs [𝜑↗→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9431→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒Modus ponens 9429, 9430
9432→→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→𝜑𝜒] into ax-2
9433→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜒Modus ponens 9431, 9432
9434→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
9435→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒Modus ponens 9341, 9434
9436→→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜒Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
9437→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜒Modus ponens 9435, 9436
9438→→→𝜑⋀𝜓𝜒→𝜑𝜒→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
9439→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒Modus ponens 6081, 9438
9440→→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
9441→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜒Modus ponens 9439, 9440
9442→¬¬⋀𝜓𝜒→𝜑𝜒Modus ponens 5479, 9441
9443→→¬¬⋀𝜓𝜒→𝜑𝜒→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-2
9444→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒Modus ponens 9442, 9443
9445→→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
9446→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒Modus ponens 9444, 9445
9447→→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜒Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜒] into ax-2
9448→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜒Modus ponens 9446, 9447
9449→𝜑→¬¬⋀𝜓𝜒𝜒Modus ponens 5487, 9448
9450→→𝜒¬¬𝜒→¬¬⋀𝜓𝜒→𝜒¬¬𝜒Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
9451→¬¬⋀𝜓𝜒→𝜒¬¬𝜒Modus ponens 9172, 9450
9452→→¬¬⋀𝜓𝜒→𝜒¬¬𝜒→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
9453→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒Modus ponens 9451, 9452
9454→→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒, 𝜓↗𝜑] into ax-1
9455→𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒Modus ponens 9453, 9454
9456→→𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒→→𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→¬¬⋀𝜓𝜒¬¬𝜒Subs [𝜓↗→¬¬⋀𝜓𝜒𝜒, 𝜒↗→¬¬⋀𝜓𝜒¬¬𝜒] into ax-2
9457→→𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→¬¬⋀𝜓𝜒¬¬𝜒Modus ponens 9455, 9456
9458→𝜑→¬¬⋀𝜓𝜒¬¬𝜒Modus ponens 9449, 9457
9459→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-3
9460→→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
9461→𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒Modus ponens 9459, 9460
9462→→𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→¬𝜒¬⋀𝜓𝜒Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜓𝜒] into ax-2
9463→→𝜑→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→¬𝜒¬⋀𝜓𝜒Modus ponens 9461, 9462
9464→𝜑→¬𝜒¬⋀𝜓𝜒Modus ponens 9458, 9463
9465→¬𝜒→𝜑¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗𝜑] into ax-1
9466→→¬𝜒→𝜑¬𝜒→¬𝜒→¬𝜒→𝜑¬𝜒Subs [𝜑↗→¬𝜒→𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1
9467→¬𝜒→¬𝜒→𝜑¬𝜒Modus ponens 9465, 9466
9468→→¬𝜒→¬𝜒→𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜑¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜑¬𝜒] into ax-2
9469→→¬𝜒¬𝜒→¬𝜒→𝜑¬𝜒Modus ponens 9467, 9468
9470→→𝜑→¬𝜒¬⋀𝜓𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜓↗¬𝜒, 𝜒↗¬⋀𝜓𝜒] into ax-2
9471→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 9464, 9470
9472→→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9473→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 9471, 9472
9474→→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
9475→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 9473, 9474
9476→¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 9465, 9475
9477→→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9478→¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5528, 9477
9479→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9480→→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9481→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9479, 9480
9482→→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
9483→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9481, 9482
9484→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 5531, 9483
9485→→¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9486→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9478, 9485
9487→→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9488→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9486, 9487
9489→→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
9490→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9488, 9489
9491→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9492→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
9493→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒Modus ponens 9491, 9492
9494→→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒] into ax-2
9495→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒Modus ponens 9493, 9494
9496→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9497→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9484, 9496
9498→→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9499→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9497, 9498
9500→→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
9501→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9499, 9500
9502→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒Modus ponens 9491, 9501
9503→→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9504→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 5556, 9503
9505→→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2
9506→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 9504, 9505
9507→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 9502, 9506
9508→→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒¬¬→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2
9509→→¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 9507, 9508
9510→¬𝜒¬¬→𝜑¬⋀𝜓𝜒Modus ponens 9476, 9509
9511→→¬𝜒¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3
9512→¬→𝜑¬⋀𝜓𝜒𝜒Modus ponens 9510, 9511
9513→→¬→𝜑¬⋀𝜓𝜒𝜒→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9514→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒Modus ponens 9512, 9513
9515→→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9516→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 9514, 9515
9517→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 5568, 9516simprr
9518→𝜑→𝜃𝜑Subs [𝜓↗𝜃] into ax-1
9519→→𝜑→𝜃𝜑→⋀𝜑𝜓→𝜑→𝜃𝜑Subs [𝜑↗→𝜑→𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
9520→⋀𝜑𝜓→𝜑→𝜃𝜑Modus ponens 9518, 9519
9521→→⋀𝜑𝜓→𝜑→𝜃𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜃𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜃𝜑] into ax-2
9522→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜃𝜑Modus ponens 9520, 9521
9523→⋀𝜑𝜓→𝜃𝜑Modus ponens simpl, 9522
9524↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into df-an
9525→¬¬𝜃𝜃Subs [𝜑↗𝜃] into notnotr
9526→𝜃→⋀𝜑𝜓𝜃Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓] into ax-1
9527→→𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→𝜃→⋀𝜑𝜓𝜃Subs [𝜑↗→𝜃→⋀𝜑𝜓𝜃, 𝜓↗¬¬𝜃] into ax-1
9528→¬¬𝜃→𝜃→⋀𝜑𝜓𝜃Modus ponens 9526, 9527
9529→→¬¬𝜃→𝜃→⋀𝜑𝜓𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑𝜓𝜃Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑𝜓𝜃] into ax-2
9530→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑𝜓𝜃Modus ponens 9528, 9529
9531→¬¬𝜃→⋀𝜑𝜓𝜃Modus ponens 9525, 9530
9532→→⋀𝜑𝜓→𝜃𝜑→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃, 𝜒↗𝜑] into ax-2
9533→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑Modus ponens 9523, 9532
9534→→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑, 𝜓↗¬¬𝜃] into ax-1
9535→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑Modus ponens 9533, 9534
9536→→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜑Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
9537→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜑Modus ponens 9535, 9536
9538→¬¬𝜃→⋀𝜑𝜓𝜑Modus ponens 9531, 9537
9539→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬𝜃] into ax-1
9540→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓Subs [𝜑↗→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9541→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓Modus ponens 9539, 9540
9542→→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→¬¬𝜃⋀𝜑𝜓] into ax-2
9543→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓Modus ponens 9541, 9542
9544→→¬¬𝜃→⋀𝜑𝜓𝜑→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2
9545→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑Modus ponens 9538, 9544
9546→→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑Subs [𝜑↗→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
9547→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑Modus ponens 9545, 9546
9548→→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃⋀𝜑𝜓, 𝜒↗→¬¬𝜃𝜑] into ax-2
9549→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜑Modus ponens 9547, 9548
9550→⋀𝜑𝜓→¬¬𝜃𝜑Modus ponens 9539, 9549
9551→→𝜑¬¬𝜑→¬¬𝜃→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜃] into ax-1
9552→¬¬𝜃→𝜑¬¬𝜑Modus ponens notnot, 9551
9553→→¬¬𝜃→𝜑¬¬𝜑→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑Subs [𝜑↗¬¬𝜃, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
9554→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑Modus ponens 9552, 9553
9555→→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑Subs [𝜑↗→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
9556→⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑Modus ponens 9554, 9555
9557→→⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→→⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→¬¬𝜃¬¬𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃𝜑, 𝜒↗→¬¬𝜃¬¬𝜑] into ax-2
9558→→⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→¬¬𝜃¬¬𝜑Modus ponens 9556, 9557
9559→⋀𝜑𝜓→¬¬𝜃¬¬𝜑Modus ponens 9550, 9558
9560→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜑] into ax-3
9561→→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃Subs [𝜑↗→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃, 𝜓↗⋀𝜑𝜓] into ax-1
9562→⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃Modus ponens 9560, 9561
9563→→⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→→⋀𝜑𝜓→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜃Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃¬¬𝜑, 𝜒↗→¬𝜑¬𝜃] into ax-2
9564→→⋀𝜑𝜓→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜃Modus ponens 9562, 9563
9565→⋀𝜑𝜓→¬𝜑¬𝜃Modus ponens 9559, 9564
9566→→⋀𝜑𝜓→¬𝜑¬𝜃→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜃] into ax-2
9567→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃Modus ponens 9565, 9566
9568→→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃Subs [𝜑↗→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9569→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃Modus ponens 9567, 9568
9570→→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜃] into ax-2
9571→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜃Modus ponens 9569, 9570
9572→¬𝜑→⋀𝜑𝜓¬𝜃Modus ponens 8680, 9571
9573→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃] into id
9574→→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9575→¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9573, 9574
9576→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃] into notnotr
9577→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9578→→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9579→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Modus ponens 9577, 9578
9580→→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜃] into ax-2
9581→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Modus ponens 9579, 9580
9582→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Modus ponens 9576, 9581
9583→→¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2
9584→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Modus ponens 9575, 9583
9585→→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9586→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Modus ponens 9584, 9585
9587→→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜃] into ax-2
9588→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃Modus ponens 9586, 9587
9589→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9590→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1
9591→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑Modus ponens 9589, 9590
9592→→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑] into ax-2
9593→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑Modus ponens 9591, 9592
9594→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2
9595→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9582, 9594
9596→→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9597→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9595, 9596
9598→→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃] into ax-2
9599→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9597, 9598
9600→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9589, 9599
9601→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→⋀𝜑𝜓¬𝜃] into ax-3
9602→→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9603→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9601, 9602
9604→→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃] into ax-2
9605→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9603, 9604
9606→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9600, 9605
9607→→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑¬¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜃, 𝜒↗¬¬→⋀𝜑𝜓¬𝜃] into ax-2
9608→→¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9606, 9607
9609→¬𝜑¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9572, 9608
9610→→¬𝜑¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃𝜑Subs [𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-3
9611→¬→⋀𝜑𝜓¬𝜃𝜑Modus ponens 9609, 9610
9612→↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into biimp
9613→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9524, 9612
9614→→¬→⋀𝜑𝜓¬𝜃𝜑→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜃] into ax-1
9615→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑Modus ponens 9611, 9614
9616→→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜑] into ax-2
9617→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑Modus ponens 9615, 9616
9618→⋀⋀𝜑𝜓𝜃𝜑Modus ponens 9613, 9617
9619→⋀⋀𝜑𝜓𝜒⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into simpl
9620→↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into bicom1
9621↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃Modus ponens 9524, 9620
9622→↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃] into biimp
9623→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃Modus ponens 9621, 9622
9624→→⋀⋀𝜑𝜓𝜃𝜑→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑Subs [𝜑↗→⋀⋀𝜑𝜓𝜃𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-1
9625→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑Modus ponens 9618, 9624
9626→→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃, 𝜒↗𝜑] into ax-2
9627→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑Modus ponens 9625, 9626
9628→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into pm3.2im
9629→→¬→⋀𝜑𝜓¬𝜃𝜑→𝜃→¬→⋀𝜑𝜓¬𝜃𝜑Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜑, 𝜓↗𝜃] into ax-1
9630→𝜃→¬→⋀𝜑𝜓¬𝜃𝜑Modus ponens 9611, 9629
9631→→𝜃→¬→⋀𝜑𝜓¬𝜃𝜑→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜑] into ax-2
9632→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑Modus ponens 9630, 9631
9633→→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑Subs [𝜑↗→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
9634→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑Modus ponens 9632, 9633
9635→→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜑Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→𝜃𝜑] into ax-2
9636→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜑Modus ponens 9634, 9635
9637→𝜃𝜃Subs [𝜑↗𝜃] into id
9638→→𝜃→⋀𝜑𝜓𝜃→𝜃→𝜃→⋀𝜑𝜓𝜃Subs [𝜑↗→𝜃→⋀𝜑𝜓𝜃, 𝜓↗𝜃] into ax-1
9639→𝜃→𝜃→⋀𝜑𝜓𝜃Modus ponens 9526, 9638
9640→→𝜃→𝜃→⋀𝜑𝜓𝜃→→𝜃𝜃→𝜃→⋀𝜑𝜓𝜃Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑𝜓𝜃] into ax-2
9641→→𝜃𝜃→𝜃→⋀𝜑𝜓𝜃Modus ponens 9639, 9640
9642→→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑, 𝜓↗𝜃] into ax-1
9643→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑Modus ponens 9533, 9642
9644→→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜑Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
9645→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜑Modus ponens 9643, 9644
9646→𝜃→⋀𝜑𝜓𝜑Modus ponens 9526, 9645
9647→⋀𝜑𝜓→𝜃⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into ax-1
9648→→⋀𝜑𝜓→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓Subs [𝜑↗→⋀𝜑𝜓→𝜃⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9649→⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓Modus ponens 9647, 9648
9650→→⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓→→⋀⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜃⋀𝜑𝜓] into ax-2
9651→→⋀⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓Modus ponens 9649, 9650
9652→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓Modus ponens 9619, 9651
9653→→𝜃→⋀𝜑𝜓𝜑→→𝜃⋀𝜑𝜓→𝜃𝜑Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2
9654→→𝜃⋀𝜑𝜓→𝜃𝜑Modus ponens 9646, 9653
9655→→→𝜃⋀𝜑𝜓→𝜃𝜑→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑Subs [𝜑↗→→𝜃⋀𝜑𝜓→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9656→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑Modus ponens 9654, 9655
9657→→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀𝜑𝜓, 𝜒↗→𝜃𝜑] into ax-2
9658→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜑Modus ponens 9656, 9657
9659→⋀⋀𝜑𝜓𝜒→𝜃𝜑Modus ponens 9652, 9658
9660→𝜃→⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9661→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗→𝜃→⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1
9662→𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃Modus ponens 9660, 9661
9663→→𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜃] into ax-2
9664→→𝜃𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃Modus ponens 9662, 9663
9665→→⋀⋀𝜑𝜓𝜒→𝜃𝜑→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜑] into ax-2
9666→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 9659, 9665
9667→→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗𝜃] into ax-1
9668→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 9666, 9667
9669→→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2
9670→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 9668, 9669
9671→𝜃→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 9660, 9670
9672→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into ax-1
9673→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9674→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒Modus ponens 9672, 9673
9675→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃⋀⋀𝜑𝜓𝜒] into ax-2
9676→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒Modus ponens 9674, 9675
9677→→𝜃→⋀⋀𝜑𝜓𝜒𝜑→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2
9678→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑Modus ponens 9671, 9677
9679→→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑Subs [𝜑↗→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9680→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑Modus ponens 9678, 9679
9681→→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜑] into ax-2
9682→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜑Modus ponens 9680, 9681
9683↔⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into df-an
9684→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗→𝜃→⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1
9685→¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃Modus ponens 9660, 9684
9686→→¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜃] into ax-2
9687→→¬¬𝜃𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃Modus ponens 9685, 9686
9688→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃Modus ponens 9525, 9687
9689→→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗¬¬𝜃] into ax-1
9690→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 9666, 9689
9691→→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2
9692→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 9690, 9691
9693→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 9688, 9692
9694→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1
9695→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9696→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒Modus ponens 9694, 9695
9697→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃⋀⋀𝜑𝜓𝜒] into ax-2
9698→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒Modus ponens 9696, 9697
9699→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑Subs [𝜑↗¬¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2
9700→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑Modus ponens 9693, 9699
9701→→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑Subs [𝜑↗→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9702→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑Modus ponens 9700, 9701
9703→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃𝜑] into ax-2
9704→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑Modus ponens 9702, 9703
9705→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑Modus ponens 9694, 9704
9706→→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑Subs [𝜑↗→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9707→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑Modus ponens 9554, 9706
9708→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃𝜑, 𝜒↗→¬¬𝜃¬¬𝜑] into ax-2
9709→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑Modus ponens 9707, 9708
9710→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑Modus ponens 9705, 9709
9711→→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃Subs [𝜑↗→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9712→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃Modus ponens 9560, 9711
9713→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜑, 𝜒↗→¬𝜑¬𝜃] into ax-2
9714→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃Modus ponens 9712, 9713
9715→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃Modus ponens 9710, 9714
9716→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9717→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1
9718→¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑Modus ponens 9716, 9717
9719→→¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜑] into ax-2
9720→→¬𝜑¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑Modus ponens 9718, 9719
9721→→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬𝜃] into ax-2
9722→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9715, 9721
9723→→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9724→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9722, 9723
9725→→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9726→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9724, 9725
9727→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9716, 9726
9728→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into id
9729→→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9730→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9728, 9729
9731→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into notnotr
9732→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9733→→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9734→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9732, 9733
9735→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9736→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9734, 9735
9737→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9731, 9736
9738→→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9739→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9730, 9738
9740→→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9741→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9739, 9740
9742→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9743→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9741, 9742
9744→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9745→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1
9746→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑Modus ponens 9744, 9745
9747→→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑] into ax-2
9748→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑Modus ponens 9746, 9747
9749→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9750→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9737, 9749
9751→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9752→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9750, 9751
9753→→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9754→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9752, 9753
9755→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9744, 9754
9756→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3
9757→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9758→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9756, 9757
9759→→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9760→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9758, 9759
9761→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9755, 9760
9762→→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9763→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9761, 9762
9764→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9727, 9763
9765→→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑Subs [𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3
9766→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑Modus ponens 9764, 9765
9767→↔⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into biimp
9768→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9683, 9767
9769→→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
9770→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑Modus ponens 9766, 9769
9771→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗𝜑] into ax-2
9772→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 9770, 9771
9773→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 9768, 9772simplll
9774→𝜓→𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗𝜃] into ax-1
9775→→𝜓→𝜃𝜓→⋀𝜑𝜓→𝜓→𝜃𝜓Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9776→⋀𝜑𝜓→𝜓→𝜃𝜓Modus ponens 9774, 9775
9777→→⋀𝜑𝜓→𝜓→𝜃𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜃𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜃𝜓] into ax-2
9778→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜃𝜓Modus ponens 9776, 9777
9779→⋀𝜑𝜓→𝜃𝜓Modus ponens simpr, 9778
9780→→⋀𝜑𝜓→𝜃𝜓→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2
9781→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓Modus ponens 9779, 9780
9782→→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓, 𝜓↗¬¬𝜃] into ax-1
9783→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓Modus ponens 9781, 9782
9784→→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜓Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
9785→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜓Modus ponens 9783, 9784
9786→¬¬𝜃→⋀𝜑𝜓𝜓Modus ponens 9531, 9785
9787→→¬¬𝜃→⋀𝜑𝜓𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
9788→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓Modus ponens 9786, 9787
9789→→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓Subs [𝜑↗→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9790→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓Modus ponens 9788, 9789
9791→→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃⋀𝜑𝜓, 𝜒↗→¬¬𝜃𝜓] into ax-2
9792→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜓Modus ponens 9790, 9791
9793→⋀𝜑𝜓→¬¬𝜃𝜓Modus ponens 9539, 9792
9794→→𝜓¬¬𝜓→¬¬𝜃→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜃] into ax-1
9795→¬¬𝜃→𝜓¬¬𝜓Modus ponens 448, 9794
9796→→¬¬𝜃→𝜓¬¬𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Subs [𝜑↗¬¬𝜃, 𝜒↗¬¬𝜓] into ax-2
9797→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Modus ponens 9795, 9796
9798→→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9799→⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Modus ponens 9797, 9798
9800→→⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→¬¬𝜃¬¬𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2
9801→→⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→¬¬𝜃¬¬𝜓Modus ponens 9799, 9800
9802→⋀𝜑𝜓→¬¬𝜃¬¬𝜓Modus ponens 9793, 9801
9803→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜓] into ax-3
9804→→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜑𝜓] into ax-1
9805→⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Modus ponens 9803, 9804
9806→→⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜑𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜃Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2
9807→→⋀𝜑𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜃Modus ponens 9805, 9806
9808→⋀𝜑𝜓→¬𝜓¬𝜃Modus ponens 9802, 9807
9809→→⋀𝜑𝜓→¬𝜓¬𝜃→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2
9810→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃Modus ponens 9808, 9809
9811→→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃Subs [𝜑↗→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9812→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃Modus ponens 9810, 9811
9813→→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜃] into ax-2
9814→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜃Modus ponens 9812, 9813
9815→¬𝜓→⋀𝜑𝜓¬𝜃Modus ponens 8871, 9814
9816→→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9817→¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9573, 9816
9818→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9819→→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9820→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Modus ponens 9818, 9819
9821→→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜃] into ax-2
9822→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Modus ponens 9820, 9821
9823→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Modus ponens 9576, 9822
9824→→¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2
9825→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Modus ponens 9817, 9824
9826→→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9827→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Modus ponens 9825, 9826
9828→→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜃] into ax-2
9829→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃Modus ponens 9827, 9828
9830→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9831→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
9832→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓Modus ponens 9830, 9831
9833→→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓] into ax-2
9834→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓Modus ponens 9832, 9833
9835→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2
9836→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9823, 9835
9837→→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9838→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9836, 9837
9839→→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃] into ax-2
9840→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9838, 9839
9841→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃Modus ponens 9830, 9840
9842→→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9843→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9601, 9842
9844→→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃] into ax-2
9845→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9843, 9844
9846→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9841, 9845
9847→→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓¬¬→⋀𝜑𝜓¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜃, 𝜒↗¬¬→⋀𝜑𝜓¬𝜃] into ax-2
9848→→¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9846, 9847
9849→¬𝜓¬¬→⋀𝜑𝜓¬𝜃Modus ponens 9815, 9848
9850→→¬𝜓¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-3
9851→¬→⋀𝜑𝜓¬𝜃𝜓Modus ponens 9849, 9850
9852→→¬→⋀𝜑𝜓¬𝜃𝜓→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜃] into ax-1
9853→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓Modus ponens 9851, 9852
9854→→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜓] into ax-2
9855→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓Modus ponens 9853, 9854
9856→⋀⋀𝜑𝜓𝜃𝜓Modus ponens 9613, 9855
9857→→⋀⋀𝜑𝜓𝜃𝜓→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓Subs [𝜑↗→⋀⋀𝜑𝜓𝜃𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-1
9858→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓Modus ponens 9856, 9857
9859→→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃, 𝜒↗𝜓] into ax-2
9860→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓Modus ponens 9858, 9859
9861→→¬→⋀𝜑𝜓¬𝜃𝜓→𝜃→¬→⋀𝜑𝜓¬𝜃𝜓Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜓, 𝜓↗𝜃] into ax-1
9862→𝜃→¬→⋀𝜑𝜓¬𝜃𝜓Modus ponens 9851, 9861
9863→→𝜃→¬→⋀𝜑𝜓¬𝜃𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜓] into ax-2
9864→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓Modus ponens 9862, 9863
9865→→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓Subs [𝜑↗→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9866→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓Modus ponens 9864, 9865
9867→→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→𝜃𝜓] into ax-2
9868→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜓Modus ponens 9866, 9867
9869→→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓, 𝜓↗𝜃] into ax-1
9870→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓Modus ponens 9781, 9869
9871→→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜓Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
9872→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜓Modus ponens 9870, 9871
9873→𝜃→⋀𝜑𝜓𝜓Modus ponens 9526, 9872
9874→→𝜃→⋀𝜑𝜓𝜓→→𝜃⋀𝜑𝜓→𝜃𝜓Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
9875→→𝜃⋀𝜑𝜓→𝜃𝜓Modus ponens 9873, 9874
9876→→→𝜃⋀𝜑𝜓→𝜃𝜓→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓Subs [𝜑↗→→𝜃⋀𝜑𝜓→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9877→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓Modus ponens 9875, 9876
9878→→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀𝜑𝜓, 𝜒↗→𝜃𝜓] into ax-2
9879→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓Modus ponens 9877, 9878
9880→⋀⋀𝜑𝜓𝜒→𝜃𝜓Modus ponens 9652, 9879
9881→→⋀⋀𝜑𝜓𝜒→𝜃𝜓→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2
9882→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 9880, 9881
9883→→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1
9884→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 9882, 9883
9885→→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2
9886→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 9884, 9885
9887→𝜃→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 9660, 9886
9888→→𝜃→⋀⋀𝜑𝜓𝜒𝜓→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2
9889→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓Modus ponens 9887, 9888
9890→→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓Subs [𝜑↗→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9891→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓Modus ponens 9889, 9890
9892→→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
9893→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜓Modus ponens 9891, 9892
9894→→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1
9895→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 9882, 9894
9896→→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2
9897→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 9895, 9896
9898→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 9688, 9897
9899→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗¬¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2
9900→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓Modus ponens 9898, 9899
9901→→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9902→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓Modus ponens 9900, 9901
9903→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2
9904→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓Modus ponens 9902, 9903
9905→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓Modus ponens 9694, 9904
9906→→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9907→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Modus ponens 9797, 9906
9908→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2
9909→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓Modus ponens 9907, 9908
9910→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓Modus ponens 9905, 9909
9911→→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9912→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Modus ponens 9803, 9911
9913→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2
9914→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃Modus ponens 9912, 9913
9915→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃Modus ponens 9910, 9914
9916→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9917→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
9918→¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓Modus ponens 9916, 9917
9919→→¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜓] into ax-2
9920→→¬𝜓¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓Modus ponens 9918, 9919
9921→→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2
9922→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9915, 9921
9923→→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9924→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9922, 9923
9925→→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9926→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9924, 9925
9927→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9916, 9926
9928→→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9929→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9728, 9928
9930→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9931→→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9932→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9930, 9931
9933→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9934→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9932, 9933
9935→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9731, 9934
9936→→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9937→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9929, 9936
9938→→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9939→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9937, 9938
9940→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9941→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9939, 9940
9942→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9943→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
9944→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓Modus ponens 9942, 9943
9945→→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓] into ax-2
9946→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓Modus ponens 9944, 9945
9947→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9948→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9935, 9947
9949→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9950→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9948, 9949
9951→→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9952→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9950, 9951
9953→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9942, 9952
9954→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9955→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9756, 9954
9956→→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9957→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9955, 9956
9958→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9953, 9957
9959→→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9960→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9958, 9959
9961→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃Modus ponens 9927, 9960
9962→→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3
9963→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓Modus ponens 9961, 9962
9964→→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
9965→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓Modus ponens 9963, 9964
9966→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2
9967→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 9965, 9966
9968→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 9768, 9967simpllr
9969→→𝜓→𝜃𝜓→⋀𝜓𝜒→𝜓→𝜃𝜓Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
9970→⋀𝜓𝜒→𝜓→𝜃𝜓Modus ponens 9774, 9969
9971→→⋀𝜓𝜒→𝜓→𝜃𝜓→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜃𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
9972→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜃𝜓Modus ponens 9970, 9971
9973→⋀𝜓𝜒→𝜃𝜓Modus ponens 6072, 9972
9974↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into df-an
9975→𝜃→⋀𝜓𝜒𝜃Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒] into ax-1
9976→→𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀𝜓𝜒𝜃Subs [𝜑↗→𝜃→⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1
9977→¬¬𝜃→𝜃→⋀𝜓𝜒𝜃Modus ponens 9975, 9976
9978→→¬¬𝜃→𝜃→⋀𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜓𝜒𝜃Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜓𝜒𝜃] into ax-2
9979→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜓𝜒𝜃Modus ponens 9977, 9978
9980→¬¬𝜃→⋀𝜓𝜒𝜃Modus ponens 9525, 9979
9981→→⋀𝜓𝜒→𝜃𝜓→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2
9982→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓Modus ponens 9973, 9981
9983→→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1
9984→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓Modus ponens 9982, 9983
9985→→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜓Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
9986→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜓Modus ponens 9984, 9985
9987→¬¬𝜃→⋀𝜓𝜒𝜓Modus ponens 9980, 9986
9988→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1
9989→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9990→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒Modus ponens 9988, 9989
9991→→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→¬¬𝜃⋀𝜓𝜒] into ax-2
9992→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒Modus ponens 9990, 9991
9993→→¬¬𝜃→⋀𝜓𝜒𝜓→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
9994→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓Modus ponens 9987, 9993
9995→→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
9996→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓Modus ponens 9994, 9995
9997→→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2
9998→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜓Modus ponens 9996, 9997
9999→⋀𝜓𝜒→¬¬𝜃𝜓Modus ponens 9988, 9998
10000→→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
10001→⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Modus ponens 9797, 10000
10002→→⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→¬¬𝜃¬¬𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2
10003→→⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→¬¬𝜃¬¬𝜓Modus ponens 10001, 10002
10004→⋀𝜓𝜒→¬¬𝜃¬¬𝜓Modus ponens 9999, 10003
10005→→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-1
10006→⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Modus ponens 9803, 10005
10007→→⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜃Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2
10008→→⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜃Modus ponens 10006, 10007
10009→⋀𝜓𝜒→¬𝜓¬𝜃Modus ponens 10004, 10008
10010→→⋀𝜓𝜒→¬𝜓¬𝜃→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2
10011→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃Modus ponens 10009, 10010
10012→→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃Subs [𝜑↗→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10013→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃Modus ponens 10011, 10012
10014→→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜃] into ax-2
10015→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜃Modus ponens 10013, 10014
10016→¬𝜓→⋀𝜓𝜒¬𝜃Modus ponens 8964, 10015
10017→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃] into id
10018→→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10019→¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10017, 10018
10020→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃] into notnotr
10021→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10022→→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10023→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Modus ponens 10021, 10022
10024→→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜃] into ax-2
10025→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Modus ponens 10023, 10024
10026→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Modus ponens 10020, 10025
10027→→¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10028→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Modus ponens 10019, 10027
10029→→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10030→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Modus ponens 10028, 10029
10031→→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜃] into ax-2
10032→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃Modus ponens 10030, 10031
10033→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10034→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
10035→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓Modus ponens 10033, 10034
10036→→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓] into ax-2
10037→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓Modus ponens 10035, 10036
10038→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10039→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10026, 10038
10040→→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10041→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10039, 10040
10042→→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃] into ax-2
10043→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10041, 10042
10044→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10033, 10043
10045→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→⋀𝜓𝜒¬𝜃] into ax-3
10046→→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10047→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10045, 10046
10048→→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃] into ax-2
10049→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10047, 10048
10050→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10044, 10049
10051→→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜓𝜒¬𝜃] into ax-2
10052→→¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10050, 10051
10053→¬𝜓¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10016, 10052
10054→→¬𝜓¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-3
10055→¬→⋀𝜓𝜒¬𝜃𝜓Modus ponens 10053, 10054
10056→↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into biimp
10057→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 9974, 10056
10058→→¬→⋀𝜓𝜒¬𝜃𝜓→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10059→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓Modus ponens 10055, 10058
10060→→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2
10061→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10059, 10060
10062→⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10057, 10061
10063→⋀𝜑⋀𝜓𝜒⋀𝜓𝜒Subs [𝜓↗⋀𝜓𝜒] into simpr
10064→↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into bicom1
10065↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃Modus ponens 9974, 10064
10066→↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into biimp
10067→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃Modus ponens 10065, 10066
10068→→⋀⋀𝜓𝜒𝜃𝜓→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓Subs [𝜑↗→⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-1
10069→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10062, 10068
10070→→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
10071→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓Modus ponens 10069, 10070
10072→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into pm3.2im
10073→→¬→⋀𝜓𝜒¬𝜃𝜓→𝜃→¬→⋀𝜓𝜒¬𝜃𝜓Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜓, 𝜓↗𝜃] into ax-1
10074→𝜃→¬→⋀𝜓𝜒¬𝜃𝜓Modus ponens 10055, 10073
10075→→𝜃→¬→⋀𝜓𝜒¬𝜃𝜓→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2
10076→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓Modus ponens 10074, 10075
10077→→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓Subs [𝜑↗→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
10078→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓Modus ponens 10076, 10077
10079→→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→𝜃𝜓] into ax-2
10080→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜓Modus ponens 10078, 10079
10081→→𝜃→⋀𝜓𝜒𝜃→𝜃→𝜃→⋀𝜓𝜒𝜃Subs [𝜑↗→𝜃→⋀𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1
10082→𝜃→𝜃→⋀𝜓𝜒𝜃Modus ponens 9975, 10081
10083→→𝜃→𝜃→⋀𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀𝜓𝜒𝜃Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜓𝜒𝜃] into ax-2
10084→→𝜃𝜃→𝜃→⋀𝜓𝜒𝜃Modus ponens 10082, 10083
10085→→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1
10086→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓Modus ponens 9982, 10085
10087→→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜓Subs [𝜑↗𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
10088→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜓Modus ponens 10086, 10087
10089→𝜃→⋀𝜓𝜒𝜓Modus ponens 9975, 10088
10090→⋀𝜓𝜒→𝜃⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into ax-1
10091→→⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→𝜃⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10092→⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒Modus ponens 10090, 10091
10093→→⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜃⋀𝜓𝜒] into ax-2
10094→→⋀𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒Modus ponens 10092, 10093
10095→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒Modus ponens 10063, 10094
10096→→𝜃→⋀𝜓𝜒𝜓→→𝜃⋀𝜓𝜒→𝜃𝜓Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10097→→𝜃⋀𝜓𝜒→𝜃𝜓Modus ponens 10089, 10096
10098→→→𝜃⋀𝜓𝜒→𝜃𝜓→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓Subs [𝜑↗→→𝜃⋀𝜓𝜒→𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10099→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓Modus ponens 10097, 10098
10100→→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
10101→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓Modus ponens 10099, 10100
10102→⋀𝜑⋀𝜓𝜒→𝜃𝜓Modus ponens 10095, 10101
10103→𝜃→⋀𝜑⋀𝜓𝜒𝜃Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10104→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃Subs [𝜑↗→𝜃→⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1
10105→𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃Modus ponens 10103, 10104
10106→→𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜃] into ax-2
10107→→𝜃𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃Modus ponens 10105, 10106
10108→→⋀𝜑⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2
10109→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 10102, 10108
10110→→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1
10111→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 10109, 10110
10112→→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2
10113→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 10111, 10112
10114→𝜃→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 10103, 10113
10115→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into ax-1
10116→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10117→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒Modus ponens 10115, 10116
10118→→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃⋀𝜑⋀𝜓𝜒] into ax-2
10119→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒Modus ponens 10117, 10118
10120→→𝜃→⋀𝜑⋀𝜓𝜒𝜓→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10121→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓Modus ponens 10114, 10120
10122→→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓Subs [𝜑↗→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10123→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓Modus ponens 10121, 10122
10124→→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
10125→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓Modus ponens 10123, 10124
10126↔⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into df-an
10127→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃Subs [𝜑↗→𝜃→⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1
10128→¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃Modus ponens 10103, 10127
10129→→¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜃] into ax-2
10130→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃Modus ponens 10128, 10129
10131→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃Modus ponens 9525, 10130
10132→→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1
10133→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 10109, 10132
10134→→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2
10135→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 10133, 10134
10136→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓Modus ponens 10131, 10135
10137→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1
10138→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10139→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒Modus ponens 10137, 10138
10140→→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃⋀𝜑⋀𝜓𝜒] into ax-2
10141→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒Modus ponens 10139, 10140
10142→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10143→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓Modus ponens 10136, 10142
10144→→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10145→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓Modus ponens 10143, 10144
10146→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2
10147→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓Modus ponens 10145, 10146
10148→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓Modus ponens 10137, 10147
10149→→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10150→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓Modus ponens 9797, 10149
10151→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2
10152→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓Modus ponens 10150, 10151
10153→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓Modus ponens 10148, 10152
10154→→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10155→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃Modus ponens 9803, 10154
10156→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2
10157→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃Modus ponens 10155, 10156
10158→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃Modus ponens 10153, 10157
10159→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10160→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓Subs [𝜑↗→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
10161→¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓Modus ponens 10159, 10160
10162→→¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜓] into ax-2
10163→→¬𝜓¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓Modus ponens 10161, 10162
10164→→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2
10165→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10158, 10164
10166→→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10167→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10165, 10166
10168→→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10169→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10167, 10168
10170→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10159, 10169
10171→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into id
10172→→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10173→¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10171, 10172
10174→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into notnotr
10175→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10176→→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10177→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10175, 10176
10178→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10179→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10177, 10178
10180→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10174, 10179
10181→→¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10182→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10173, 10181
10183→→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10184→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10182, 10183
10185→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10186→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10184, 10185
10187→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10188→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
10189→¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓Modus ponens 10187, 10188
10190→→¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓] into ax-2
10191→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓Modus ponens 10189, 10190
10192→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10193→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10180, 10192
10194→→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10195→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10193, 10194
10196→→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10197→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10195, 10196
10198→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10187, 10197
10199→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3
10200→→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10201→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10199, 10200
10202→→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10203→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10201, 10202
10204→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10198, 10203
10205→→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10206→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10204, 10205
10207→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10170, 10206
10208→→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3
10209→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓Modus ponens 10207, 10208
10210→↔⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into biimp
10211→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10126, 10210
10212→→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀𝜑⋀𝜓𝜒𝜃] into ax-1
10213→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓Modus ponens 10209, 10212
10214→→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜓Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2
10215→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜓Modus ponens 10213, 10214
10216→⋀⋀𝜑⋀𝜓𝜒𝜃𝜓Modus ponens 10211, 10215simplrl
10217→𝜒→𝜃𝜒Subs [𝜑↗𝜒, 𝜓↗𝜃] into ax-1
10218→→𝜒→𝜃𝜒→⋀𝜓𝜒→𝜒→𝜃𝜒Subs [𝜑↗→𝜒→𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10219→⋀𝜓𝜒→𝜒→𝜃𝜒Modus ponens 10217, 10218
10220→→⋀𝜓𝜒→𝜒→𝜃𝜒→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜃𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗→𝜃𝜒] into ax-2
10221→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜃𝜒Modus ponens 10219, 10220
10222→⋀𝜓𝜒→𝜃𝜒Modus ponens 6077, 10221
10223→→⋀𝜓𝜒→𝜃𝜒→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into ax-2
10224→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒Modus ponens 10222, 10223
10225→→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜃] into ax-1
10226→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒Modus ponens 10224, 10225
10227→→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜒Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
10228→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜒Modus ponens 10226, 10227
10229→¬¬𝜃→⋀𝜓𝜒𝜒Modus ponens 9980, 10228
10230→→¬¬𝜃→⋀𝜓𝜒𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-2
10231→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒Modus ponens 10229, 10230
10232→→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒Subs [𝜑↗→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10233→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒Modus ponens 10231, 10232
10234→→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜒] into ax-2
10235→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜒Modus ponens 10233, 10234
10236→⋀𝜓𝜒→¬¬𝜃𝜒Modus ponens 9988, 10235
10237→→𝜒¬¬𝜒→¬¬𝜃→𝜒¬¬𝜒Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜃] into ax-1
10238→¬¬𝜃→𝜒¬¬𝜒Modus ponens 9172, 10237
10239→→¬¬𝜃→𝜒¬¬𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒Subs [𝜑↗¬¬𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
10240→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒Modus ponens 10238, 10239
10241→→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒Subs [𝜑↗→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10242→⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒Modus ponens 10240, 10241
10243→→⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→→⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→¬¬𝜃¬¬𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜒, 𝜒↗→¬¬𝜃¬¬𝜒] into ax-2
10244→→⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→¬¬𝜃¬¬𝜒Modus ponens 10242, 10243
10245→⋀𝜓𝜒→¬¬𝜃¬¬𝜒Modus ponens 10236, 10244
10246→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜒] into ax-3
10247→→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃Subs [𝜑↗→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-1
10248→⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃Modus ponens 10246, 10247
10249→→⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→→⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜃Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜒, 𝜒↗→¬𝜒¬𝜃] into ax-2
10250→→⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜃Modus ponens 10248, 10249
10251→⋀𝜓𝜒→¬𝜒¬𝜃Modus ponens 10245, 10250
10252→→⋀𝜓𝜒→¬𝜒¬𝜃→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜃] into ax-2
10253→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃Modus ponens 10251, 10252
10254→→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃Subs [𝜑↗→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10255→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃Modus ponens 10253, 10254
10256→→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜃] into ax-2
10257→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜃Modus ponens 10255, 10256
10258→¬𝜒→⋀𝜓𝜒¬𝜃Modus ponens 9369, 10257
10259→→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10260→¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10017, 10259
10261→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10262→→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10263→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Modus ponens 10261, 10262
10264→→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜃] into ax-2
10265→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Modus ponens 10263, 10264
10266→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Modus ponens 10020, 10265
10267→→¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10268→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Modus ponens 10260, 10267
10269→→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10270→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Modus ponens 10268, 10269
10271→→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜃] into ax-2
10272→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃Modus ponens 10270, 10271
10273→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10274→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10275→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒Modus ponens 10273, 10274
10276→→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒] into ax-2
10277→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒Modus ponens 10275, 10276
10278→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10279→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10266, 10278
10280→→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10281→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10279, 10280
10282→→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃] into ax-2
10283→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10281, 10282
10284→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃Modus ponens 10273, 10283
10285→→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10286→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10045, 10285
10287→→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃] into ax-2
10288→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10286, 10287
10289→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10284, 10288
10290→→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜓𝜒¬𝜃] into ax-2
10291→→¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10289, 10290
10292→¬𝜒¬¬→⋀𝜓𝜒¬𝜃Modus ponens 10258, 10291
10293→→¬𝜒¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃𝜒Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-3
10294→¬→⋀𝜓𝜒¬𝜃𝜒Modus ponens 10292, 10293
10295→→¬→⋀𝜓𝜒¬𝜃𝜒→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10296→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒Modus ponens 10294, 10295
10297→→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10298→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10296, 10297
10299→⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10057, 10298
10300→→⋀⋀𝜓𝜒𝜃𝜒→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒Subs [𝜑↗→⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-1
10301→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10299, 10300
10302→→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-2
10303→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒Modus ponens 10301, 10302
10304→→¬→⋀𝜓𝜒¬𝜃𝜒→𝜃→¬→⋀𝜓𝜒¬𝜃𝜒Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜒, 𝜓↗𝜃] into ax-1
10305→𝜃→¬→⋀𝜓𝜒¬𝜃𝜒Modus ponens 10294, 10304
10306→→𝜃→¬→⋀𝜓𝜒¬𝜃𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10307→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒Modus ponens 10305, 10306
10308→→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒Subs [𝜑↗→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10309→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒Modus ponens 10307, 10308
10310→→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→𝜃𝜒] into ax-2
10311→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜒Modus ponens 10309, 10310
10312→→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒, 𝜓↗𝜃] into ax-1
10313→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒Modus ponens 10224, 10312
10314→→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜒Subs [𝜑↗𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
10315→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜒Modus ponens 10313, 10314
10316→𝜃→⋀𝜓𝜒𝜒Modus ponens 9975, 10315
10317→→𝜃→⋀𝜓𝜒𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒] into ax-2
10318→→𝜃⋀𝜓𝜒→𝜃𝜒Modus ponens 10316, 10317
10319→→→𝜃⋀𝜓𝜒→𝜃𝜒→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒Subs [𝜑↗→→𝜃⋀𝜓𝜒→𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10320→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒Modus ponens 10318, 10319
10321→→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜓𝜒, 𝜒↗→𝜃𝜒] into ax-2
10322→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒Modus ponens 10320, 10321
10323→⋀𝜑⋀𝜓𝜒→𝜃𝜒Modus ponens 10095, 10322
10324→→⋀𝜑⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into ax-2
10325→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 10323, 10324
10326→→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗𝜃] into ax-1
10327→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 10325, 10326
10328→→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜒Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜒] into ax-2
10329→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 10327, 10328
10330→𝜃→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 10103, 10329
10331→→𝜃→⋀𝜑⋀𝜓𝜒𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2
10332→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒Modus ponens 10330, 10331
10333→→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒Subs [𝜑↗→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10334→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒Modus ponens 10332, 10333
10335→→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃𝜒] into ax-2
10336→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒Modus ponens 10334, 10335
10337→→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜃] into ax-1
10338→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 10325, 10337
10339→→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜒] into ax-2
10340→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 10338, 10339
10341→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒Modus ponens 10131, 10340
10342→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2
10343→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒Modus ponens 10341, 10342
10344→→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒Subs [𝜑↗→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10345→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒Modus ponens 10343, 10344
10346→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜒] into ax-2
10347→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒Modus ponens 10345, 10346
10348→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒Modus ponens 10137, 10347
10349→→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒Subs [𝜑↗→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10350→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒Modus ponens 10240, 10349
10351→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜒, 𝜒↗→¬¬𝜃¬¬𝜒] into ax-2
10352→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒Modus ponens 10350, 10351
10353→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒Modus ponens 10348, 10352
10354→→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃Subs [𝜑↗→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10355→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃Modus ponens 10246, 10354
10356→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜒, 𝜒↗→¬𝜒¬𝜃] into ax-2
10357→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃Modus ponens 10355, 10356
10358→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃Modus ponens 10353, 10357
10359→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10360→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒Subs [𝜑↗→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
10361→¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒Modus ponens 10359, 10360
10362→→¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜒] into ax-2
10363→→¬𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒Modus ponens 10361, 10362
10364→→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜃] into ax-2
10365→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10358, 10364
10366→→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10367→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10365, 10366
10368→→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10369→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10367, 10368
10370→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10359, 10369
10371→→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10372→¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10171, 10371
10373→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10374→→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10375→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10373, 10374
10376→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10377→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10375, 10376
10378→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10174, 10377
10379→→¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10380→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10372, 10379
10381→→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10382→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10380, 10381
10383→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10384→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10382, 10383
10385→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10386→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10387→¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒Modus ponens 10385, 10386
10388→→¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒] into ax-2
10389→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒Modus ponens 10387, 10388
10390→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10391→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10378, 10390
10392→→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10393→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10391, 10392
10394→→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10395→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10393, 10394
10396→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10385, 10395
10397→→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10398→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10199, 10397
10399→→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10400→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10398, 10399
10401→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10396, 10400
10402→→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10403→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10401, 10402
10404→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃Modus ponens 10370, 10403
10405→→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3
10406→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒Modus ponens 10404, 10405
10407→→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒, 𝜓↗⋀⋀𝜑⋀𝜓𝜒𝜃] into ax-1
10408→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒Modus ponens 10406, 10407
10409→→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜒Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10410→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜒Modus ponens 10408, 10409
10411→⋀⋀𝜑⋀𝜓𝜒𝜃𝜒Modus ponens 10211, 10410simplrr
10412→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into simpl
10413→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10414→⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 5001, 10413
10415→→⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
10416→→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10414, 10415
10417→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10412, 10416
10418↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into df-an
10419→𝜑→⋀⋀𝜓𝜒𝜃𝜑Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10420→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑Subs [𝜑↗→𝜑→⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜑] into ax-1
10421→¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10419, 10420
10422→→¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃𝜑] into ax-2
10423→→¬¬𝜑𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10421, 10422
10424→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑Modus ponens notnotr, 10423
10425→→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10426→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10417, 10425
10427→→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1
10428→¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10426, 10427
10429→→¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2
10430→→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10428, 10429
10431→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10424, 10430
10432→⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃Subs [𝜑↗⋀⋀𝜓𝜒𝜃] into id
10433→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜑] into ax-1
10434→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃Subs [𝜑↗→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10435→⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃Modus ponens 10433, 10434
10436→→⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→→⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗→¬¬𝜑⋀⋀𝜓𝜒𝜃] into ax-2
10437→→⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃Modus ponens 10435, 10436
10438→→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒Subs [𝜑↗¬¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2
10439→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒Modus ponens 10431, 10438
10440→→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10441→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒Modus ponens 10439, 10440
10442→→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗→¬¬𝜑⋀𝜓𝜒] into ax-2
10443→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒Modus ponens 10441, 10442
10444→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒Modus ponens 10433, 10443
10445→⋀𝜓𝜒¬¬⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒] into notnot
10446→→⋀𝜓𝜒¬¬⋀𝜓𝜒→¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒¬¬⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1
10447→¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒Modus ponens 10445, 10446
10448→→¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒, 𝜒↗¬¬⋀𝜓𝜒] into ax-2
10449→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒Modus ponens 10447, 10448
10450→→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10451→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒Modus ponens 10449, 10450
10452→→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑¬¬⋀𝜓𝜒] into ax-2
10453→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒Modus ponens 10451, 10452
10454→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒Modus ponens 10444, 10453
10455→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-3
10456→→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑Subs [𝜑↗→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10457→⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑Modus ponens 10455, 10456
10458→→⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑→→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑¬¬⋀𝜓𝜒, 𝜒↗→¬⋀𝜓𝜒¬𝜑] into ax-2
10459→→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑Modus ponens 10457, 10458
10460→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑Modus ponens 10454, 10459
10461→¬⋀𝜓𝜒¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒] into id
10462→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10463→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Subs [𝜑↗→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1
10464→¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Modus ponens 10462, 10463
10465→→¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒] into ax-2
10466→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Modus ponens 10464, 10465
10467→→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬𝜑] into ax-2
10468→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10460, 10467
10469→→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10470→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10468, 10469
10471→→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜒↗→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10472→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10470, 10471
10473→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10462, 10472
10474→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into id
10475→→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10476→¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10474, 10475
10477→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into notnotr
10478→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10479→→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1
10480→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10478, 10479
10481→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10482→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10480, 10481
10483→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10477, 10482
10484→→¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10485→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10476, 10484
10486→→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1
10487→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10485, 10486
10488→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10489→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10487, 10488
10490→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1
10491→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒Subs [𝜑↗→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1
10492→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒Modus ponens 10490, 10491
10493→→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒] into ax-2
10494→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒Modus ponens 10492, 10493
10495→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10496→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10483, 10495
10497→→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10498→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10496, 10497
10499→→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10500→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10498, 10499
10501→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10490, 10500
10502→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-3
10503→→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10504→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10502, 10503
10505→→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10506→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10504, 10505
10507→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10501, 10506
10508→→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10509→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10507, 10508
10510→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10473, 10509
10511→→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-3
10512→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒Modus ponens 10510, 10511
10513→↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into biimp
10514→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Modus ponens 10418, 10513
10515→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑] into ax-1
10516→⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒Modus ponens 10512, 10515
10517→→⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10518→→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒Modus ponens 10516, 10517
10519→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒Modus ponens 10514, 10518
10520→↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into bicom1
10521↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10418, 10520
10522→↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑] into biimp
10523→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10521, 10522
10524→→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒Subs [𝜑↗→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1
10525→¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒Modus ponens 10519, 10524
10526→→¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10527→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒Modus ponens 10525, 10526
10528→⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into pm3.2im
10529→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10530→𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒Modus ponens 10512, 10529
10531→→𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒Subs [𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10532→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒Modus ponens 10530, 10531
10533→→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10534→⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒Modus ponens 10532, 10533
10535→→⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
10536→→⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10534, 10535
10537→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑Subs [𝜑↗→𝜑→⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
10538→𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10419, 10537
10539→→𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑Subs [𝜓↗𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃𝜑] into ax-2
10540→→𝜑𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10538, 10539
10541→→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10542→𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10426, 10541
10543→→𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜓↗→⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2
10544→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10542, 10543
10545→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10419, 10544
10546↔⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into df-an
10547→¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃Subs [𝜑↗⋀⋀𝜓𝜒𝜃] into notnotr
10548→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-1
10549→→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃Subs [𝜑↗→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1
10550→¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃Modus ponens 10548, 10549
10551→→¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→→¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗→𝜑⋀⋀𝜓𝜒𝜃] into ax-2
10552→→¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃Modus ponens 10550, 10551
10553→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃Modus ponens 10547, 10552
10554→→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Subs [𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2
10555→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10545, 10554
10556→→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1
10557→¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10555, 10556
10558→→¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
10559→→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10557, 10558
10560→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10553, 10559
10561→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑Subs [𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1
10562→→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑Subs [𝜑↗→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
10563→𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10561, 10562
10564→→𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃𝜑] into ax-2
10565→→𝜑𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10563, 10564
10566→→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10567→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10560, 10566
10568→→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10569→𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10567, 10568
10570→→𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2
10571→→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10569, 10570
10572→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10561, 10571
10573→→⋀𝜓𝜒¬¬⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒¬¬⋀𝜓𝜒, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1
10574→¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒Modus ponens 10445, 10573
10575→→¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗¬¬⋀𝜓𝜒] into ax-2
10576→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒Modus ponens 10574, 10575
10577→→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10578→𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒Modus ponens 10576, 10577
10579→→𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒] into ax-2
10580→→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒Modus ponens 10578, 10579
10581→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒Modus ponens 10572, 10580
10582→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-3
10583→→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-1
10584→𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃Modus ponens 10582, 10583
10585→→𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒, 𝜒↗→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃] into ax-2
10586→→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃Modus ponens 10584, 10585
10587→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃Modus ponens 10581, 10586
10588→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10589→→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1
10590→¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒Modus ponens 10588, 10589
10591→→¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
10592→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒Modus ponens 10590, 10591
10593→→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜓↗¬⋀𝜓𝜒, 𝜒↗¬⋀⋀𝜓𝜒𝜃] into ax-2
10594→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10587, 10593
10595→→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10596→¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10594, 10595
10597→→¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10598→→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10596, 10597
10599→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10588, 10598
10600→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into id
10601→→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10602→¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10600, 10601
10603→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into notnotr
10604→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10605→→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1
10606→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10604, 10605
10607→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10608→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10606, 10607
10609→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10603, 10608
10610→→¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10611→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10602, 10610
10612→→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1
10613→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10611, 10612
10614→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10615→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10613, 10614
10616→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1
10617→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Subs [𝜑↗→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1
10618→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Modus ponens 10616, 10617
10619→→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒] into ax-2
10620→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒Modus ponens 10618, 10619
10621→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10622→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10609, 10621
10623→→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10624→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10622, 10623
10625→→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10626→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10624, 10625
10627→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10616, 10626
10628→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-3
10629→→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10630→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10628, 10629
10631→→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10632→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10630, 10631
10633→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10627, 10632
10634→→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10635→→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10633, 10634
10636→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10599, 10635
10637→→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-3
10638→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10636, 10637
10639→↔⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into biimp
10640→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃Modus ponens 10546, 10639
10641→→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10642→⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10638, 10641
10643→→⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2
10644→→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10642, 10643
10645→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒Modus ponens 10640, 10644
10646→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into simpl
10647→→⋀𝜑⋀𝜓𝜒𝜓→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Subs [𝜑↗→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1
10648→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓Modus ponens simprl, 10647
10649→→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10650→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓Modus ponens 10648, 10649
10651→→¬→𝜑¬⋀𝜓𝜒𝜓→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
10652→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓Modus ponens 9112, 10651
10653→→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10654→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓Modus ponens 10652, 10653
10655→→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
10656→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓Modus ponens 10654, 10655
10657→→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜓Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
10658→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜓Modus ponens 10656, 10657
10659→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10660→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒Modus ponens 5001, 10659
10661→→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
10662→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10660, 10661
10663→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒Modus ponens 10645, 10662
10664→→→𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10665→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 6076, 10664
10666→→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
10667→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓Modus ponens 10665, 10666
10668→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓Modus ponens 10663, 10667
10669→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑Subs [𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10670→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
10671→𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10669, 10670
10672→→𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑] into ax-2
10673→→𝜑𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑Modus ponens 10671, 10672
10674→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
10675→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10668, 10674
10676→→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Subs [𝜑↗→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗𝜑] into ax-1
10677→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10675, 10676
10678→→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Subs [𝜓↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓] into ax-2
10679→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10677, 10678
10680→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10669, 10679
10681→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10682→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10680, 10681
10683→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓] into ax-2
10684→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10682, 10683
10685→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10646, 10684
10686→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃] into id
10687→→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
10688→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10685, 10687
10689→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓Modus ponens 10686, 10688simprll
10690→→⋀𝜑⋀𝜓𝜒𝜒→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒Subs [𝜑↗→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1
10691→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒Modus ponens simprr, 10690
10692→→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2
10693→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒Modus ponens 10691, 10692
10694→→¬→𝜑¬⋀𝜓𝜒𝜒→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10695→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒Modus ponens 9512, 10694
10696→→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-2
10697→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒Modus ponens 10695, 10696
10698→→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
10699→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒Modus ponens 10697, 10698
10700→→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜒Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
10701→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜒Modus ponens 10699, 10700
10702→→→𝜑⋀𝜓𝜒→𝜑𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10703→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒Modus ponens 6081, 10702
10704→→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
10705→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒Modus ponens 10703, 10704
10706→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒Modus ponens 10663, 10705
10707→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-2
10708→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10706, 10707
10709→→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Subs [𝜑↗→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1
10710→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10708, 10709
10711→→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Subs [𝜓↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒] into ax-2
10712→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10710, 10711
10713→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10669, 10712
10714→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10715→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10713, 10714
10716→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒] into ax-2
10717→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10715, 10716
10718→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10646, 10717
10719→→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-2
10720→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10718, 10719
10721→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒Modus ponens 10686, 10720simprlr
10722→⋀𝜒𝜃𝜒Subs [𝜑↗𝜒, 𝜓↗𝜃] into simpl
10723→→𝜒→𝜓𝜒→⋀𝜒𝜃→𝜒→𝜓𝜒Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10724→⋀𝜒𝜃→𝜒→𝜓𝜒Modus ponens 5362, 10723
10725→→⋀𝜒𝜃→𝜒→𝜓𝜒→→⋀𝜒𝜃𝜒→⋀𝜒𝜃→𝜓𝜒Subs [𝜑↗⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2
10726→→⋀𝜒𝜃𝜒→⋀𝜒𝜃→𝜓𝜒Modus ponens 10724, 10725
10727→⋀𝜒𝜃→𝜓𝜒Modus ponens 10722, 10726
10728↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗⋀𝜒𝜃] into df-an
10729→𝜓→⋀𝜒𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into ax-1
10730→→𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→𝜓→⋀𝜒𝜃𝜓Subs [𝜑↗→𝜓→⋀𝜒𝜃𝜓, 𝜓↗¬¬𝜓] into ax-1
10731→¬¬𝜓→𝜓→⋀𝜒𝜃𝜓Modus ponens 10729, 10730
10732→→¬¬𝜓→𝜓→⋀𝜒𝜃𝜓→→¬¬𝜓𝜓→¬¬𝜓→⋀𝜒𝜃𝜓Subs [𝜑↗¬¬𝜓, 𝜒↗→⋀𝜒𝜃𝜓] into ax-2
10733→→¬¬𝜓𝜓→¬¬𝜓→⋀𝜒𝜃𝜓Modus ponens 10731, 10732
10734→¬¬𝜓→⋀𝜒𝜃𝜓Modus ponens 570, 10733
10735→→⋀𝜒𝜃→𝜓𝜒→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒Subs [𝜑↗⋀𝜒𝜃] into ax-2
10736→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒Modus ponens 10727, 10735
10737→→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒, 𝜓↗¬¬𝜓] into ax-1
10738→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒Modus ponens 10736, 10737
10739→→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜒] into ax-2
10740→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜒Modus ponens 10738, 10739
10741→¬¬𝜓→⋀𝜒𝜃𝜒Modus ponens 10734, 10740
10742→⋀𝜒𝜃⋀𝜒𝜃Subs [𝜑↗⋀𝜒𝜃] into id
10743→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬¬𝜓] into ax-1
10744→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃Subs [𝜑↗→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
10745→⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃Modus ponens 10743, 10744
10746→→⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→→⋀𝜒𝜃⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃, 𝜒↗→¬¬𝜓⋀𝜒𝜃] into ax-2
10747→→⋀𝜒𝜃⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃Modus ponens 10745, 10746
10748→→¬¬𝜓→⋀𝜒𝜃𝜒→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-2
10749→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒Modus ponens 10741, 10748
10750→→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒Subs [𝜑↗→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10751→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒Modus ponens 10749, 10750
10752→→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜒Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜓𝜒] into ax-2
10753→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜒Modus ponens 10751, 10752
10754→⋀𝜒𝜃→¬¬𝜓𝜒Modus ponens 10743, 10753
10755→→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10756→⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒Modus ponens 9176, 10755
10757→→⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→→⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→¬¬𝜓¬¬𝜒Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓¬¬𝜒] into ax-2
10758→→⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→¬¬𝜓¬¬𝜒Modus ponens 10756, 10757
10759→⋀𝜒𝜃→¬¬𝜓¬¬𝜒Modus ponens 10754, 10758
10760→→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-1
10761→⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓Modus ponens 9182, 10760
10762→→⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→→⋀𝜒𝜃→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→¬𝜒¬𝜓Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓¬¬𝜒, 𝜒↗→¬𝜒¬𝜓] into ax-2
10763→→⋀𝜒𝜃→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→¬𝜒¬𝜓Modus ponens 10761, 10762
10764→⋀𝜒𝜃→¬𝜒¬𝜓Modus ponens 10759, 10763
10765→¬𝜒→⋀𝜒𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10766→→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒Subs [𝜑↗→¬𝜒→⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10767→¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒Modus ponens 10765, 10766
10768→→¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜒𝜃¬𝜒] into ax-2
10769→→¬𝜒¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒Modus ponens 10767, 10768
10770→→⋀𝜒𝜃→¬𝜒¬𝜓→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬𝜓] into ax-2
10771→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓Modus ponens 10764, 10770
10772→→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓Subs [𝜑↗→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10773→¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓Modus ponens 10771, 10772
10774→→¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓→→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜒𝜃¬𝜒, 𝜒↗→⋀𝜒𝜃¬𝜓] into ax-2
10775→→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜓Modus ponens 10773, 10774
10776→¬𝜒→⋀𝜒𝜃¬𝜓Modus ponens 10765, 10775
10777→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓] into id
10778→→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10779→¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 10777, 10778
10780→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓] into notnotr
10781→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10782→→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
10783→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Modus ponens 10781, 10782
10784→→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜒¬→⋀𝜒𝜃¬𝜓] into ax-2
10785→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Modus ponens 10783, 10784
10786→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Modus ponens 10780, 10785
10787→→¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2
10788→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Modus ponens 10779, 10787
10789→→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
10790→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Modus ponens 10788, 10789
10791→→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜒¬→⋀𝜒𝜃¬𝜓] into ax-2
10792→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓Modus ponens 10790, 10791
10793→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
10794→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
10795→¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒Modus ponens 10793, 10794
10796→→¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒] into ax-2
10797→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒Modus ponens 10795, 10796
10798→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2
10799→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 10786, 10798
10800→→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10801→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 10799, 10800
10802→→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓] into ax-2
10803→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 10801, 10802
10804→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 10793, 10803
10805→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→⋀𝜒𝜃¬𝜓] into ax-3
10806→→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10807→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Modus ponens 10805, 10806
10808→→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓] into ax-2
10809→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Modus ponens 10807, 10808
10810→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Modus ponens 10804, 10809
10811→→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒¬¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜒𝜃¬𝜓, 𝜒↗¬¬→⋀𝜒𝜃¬𝜓] into ax-2
10812→→¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒¬¬→⋀𝜒𝜃¬𝜓Modus ponens 10810, 10811
10813→¬𝜒¬¬→⋀𝜒𝜃¬𝜓Modus ponens 10776, 10812
10814→→¬𝜒¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-3
10815→¬→⋀𝜒𝜃¬𝜓𝜒Modus ponens 10813, 10814
10816→↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into biimp
10817→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 10728, 10816
10818→→¬→⋀𝜒𝜃¬𝜓𝜒→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜒, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-1
10819→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒Modus ponens 10815, 10818
10820→→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-2
10821→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒Modus ponens 10819, 10820
10822→⋀⋀𝜒𝜃𝜓𝜒Modus ponens 10817, 10821
10823→↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into bicom1
10824↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓Modus ponens 10728, 10823
10825→↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓] into biimp
10826→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓Modus ponens 10824, 10825
10827→→⋀⋀𝜒𝜃𝜓𝜒→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒Subs [𝜑↗→⋀⋀𝜒𝜃𝜓𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-1
10828→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒Modus ponens 10822, 10827
10829→→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-2
10830→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒Modus ponens 10828, 10829
10831→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗⋀𝜒𝜃] into pm3.2im
10832→→¬→⋀𝜒𝜃¬𝜓𝜒→𝜓→¬→⋀𝜒𝜃¬𝜓𝜒Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜒] into ax-1
10833→𝜓→¬→⋀𝜒𝜃¬𝜓𝜒Modus ponens 10815, 10832
10834→→𝜓→¬→⋀𝜒𝜃¬𝜓𝜒→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-2
10835→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒Modus ponens 10833, 10834
10836→→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒Subs [𝜑↗→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10837→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒Modus ponens 10835, 10836
10838→→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜒Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→𝜓𝜒] into ax-2
10839→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜒Modus ponens 10837, 10838
10840→→𝜓→⋀𝜒𝜃𝜓→𝜓→𝜓→⋀𝜒𝜃𝜓Subs [𝜑↗→𝜓→⋀𝜒𝜃𝜓] into ax-1
10841→𝜓→𝜓→⋀𝜒𝜃𝜓Modus ponens 10729, 10840
10842→→𝜓→𝜓→⋀𝜒𝜃𝜓→→𝜓𝜓→𝜓→⋀𝜒𝜃𝜓Subs [𝜑↗𝜓, 𝜒↗→⋀𝜒𝜃𝜓] into ax-2
10843→→𝜓𝜓→𝜓→⋀𝜒𝜃𝜓Modus ponens 10841, 10842
10844→→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒] into ax-1
10845→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒Modus ponens 10736, 10844
10846→→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜒Subs [𝜑↗𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜒] into ax-2
10847→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜒Modus ponens 10845, 10846
10848→𝜓→⋀𝜒𝜃𝜒Modus ponens 10729, 10847
10849↔⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into df-an
10850→¬¬⋀𝜒𝜃⋀𝜒𝜃Subs [𝜑↗⋀𝜒𝜃] into notnotr
10851→⋀𝜒𝜃→𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜒𝜃] into ax-1
10852→→⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃Subs [𝜑↗→⋀𝜒𝜃→𝜓⋀𝜒𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
10853→¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃Modus ponens 10851, 10852
10854→→¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃→→¬¬⋀𝜒𝜃⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃, 𝜒↗→𝜓⋀𝜒𝜃] into ax-2
10855→→¬¬⋀𝜒𝜃⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃Modus ponens 10853, 10854
10856→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃Modus ponens 10850, 10855
10857→→𝜓→⋀𝜒𝜃𝜒→→𝜓⋀𝜒𝜃→𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into ax-2
10858→→𝜓⋀𝜒𝜃→𝜓𝜒Modus ponens 10848, 10857
10859→→→𝜓⋀𝜒𝜃→𝜓𝜒→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒Subs [𝜑↗→→𝜓⋀𝜒𝜃→𝜓𝜒, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
10860→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒Modus ponens 10858, 10859
10861→→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜒Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗→𝜓⋀𝜒𝜃, 𝜒↗→𝜓𝜒] into ax-2
10862→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜒Modus ponens 10860, 10861
10863→¬¬⋀𝜒𝜃→𝜓𝜒Modus ponens 10856, 10862
10864→𝜓→¬¬⋀𝜒𝜃𝜓Subs [𝜑↗𝜓, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
10865→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→𝜓→¬¬⋀𝜒𝜃𝜓Subs [𝜑↗→𝜓→¬¬⋀𝜒𝜃𝜓] into ax-1
10866→𝜓→𝜓→¬¬⋀𝜒𝜃𝜓Modus ponens 10864, 10865
10867→→𝜓→𝜓→¬¬⋀𝜒𝜃𝜓→→𝜓𝜓→𝜓→¬¬⋀𝜒𝜃𝜓Subs [𝜑↗𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜓] into ax-2
10868→→𝜓𝜓→𝜓→¬¬⋀𝜒𝜃𝜓Modus ponens 10866, 10867
10869→→¬¬⋀𝜒𝜃→𝜓𝜒→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒Subs [𝜑↗¬¬⋀𝜒𝜃] into ax-2
10870→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒Modus ponens 10863, 10869
10871→→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒] into ax-1
10872→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒Modus ponens 10870, 10871
10873→→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜒] into ax-2
10874→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜒Modus ponens 10872, 10873
10875→𝜓→¬¬⋀𝜒𝜃𝜒Modus ponens 10864, 10874
10876→→𝜒¬¬𝜒→¬¬⋀𝜒𝜃→𝜒¬¬𝜒Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
10877→¬¬⋀𝜒𝜃→𝜒¬¬𝜒Modus ponens 9172, 10876
10878→→¬¬⋀𝜒𝜃→𝜒¬¬𝜒→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
10879→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒Modus ponens 10877, 10878
10880→→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒] into ax-1
10881→𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒Modus ponens 10879, 10880
10882→→𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒→→𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→¬¬⋀𝜒𝜃¬¬𝜒Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜒, 𝜒↗→¬¬⋀𝜒𝜃¬¬𝜒] into ax-2
10883→→𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→¬¬⋀𝜒𝜃¬¬𝜒Modus ponens 10881, 10882
10884→𝜓→¬¬⋀𝜒𝜃¬¬𝜒Modus ponens 10875, 10883
10885→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃Subs [𝜑↗¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-3
10886→→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃→𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃Subs [𝜑↗→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃] into ax-1
10887→𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃Modus ponens 10885, 10886
10888→→𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃→→𝜓→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→¬𝜒¬⋀𝜒𝜃Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜒𝜃] into ax-2
10889→→𝜓→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→¬𝜒¬⋀𝜒𝜃Modus ponens 10887, 10888
10890→𝜓→¬𝜒¬⋀𝜒𝜃Modus ponens 10884, 10889
10891→→𝜓→¬𝜒¬⋀𝜒𝜃→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃Subs [𝜑↗𝜓, 𝜓↗¬𝜒, 𝜒↗¬⋀𝜒𝜃] into ax-2
10892→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃Modus ponens 10890, 10891
10893→→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃Subs [𝜑↗→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10894→¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃Modus ponens 10892, 10893
10895→→¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗→𝜓¬⋀𝜒𝜃] into ax-2
10896→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬⋀𝜒𝜃Modus ponens 10894, 10895
10897→¬𝜒→𝜓¬⋀𝜒𝜃Modus ponens 9284, 10896
10898→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃] into id
10899→→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10900→¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 10898, 10899
10901→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃] into notnotr
10902→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10903→→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
10904→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Modus ponens 10902, 10903
10905→→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜓¬⋀𝜒𝜃] into ax-2
10906→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Modus ponens 10904, 10905
10907→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Modus ponens 10901, 10906
10908→→¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2
10909→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Modus ponens 10900, 10908
10910→→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
10911→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Modus ponens 10909, 10910
10912→→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜓¬⋀𝜒𝜃] into ax-2
10913→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃Modus ponens 10911, 10912
10914→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
10915→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10916→¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒Modus ponens 10914, 10915
10917→→¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒] into ax-2
10918→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒Modus ponens 10916, 10917
10919→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2
10920→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 10907, 10919
10921→→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10922→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 10920, 10921
10923→→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2
10924→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 10922, 10923
10925→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 10914, 10924
10926→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→𝜓¬⋀𝜒𝜃] into ax-3
10927→→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10928→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Modus ponens 10926, 10927
10929→→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃] into ax-2
10930→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Modus ponens 10928, 10929
10931→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Modus ponens 10925, 10930
10932→→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒¬¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬⋀𝜒𝜃, 𝜒↗¬¬→𝜓¬⋀𝜒𝜃] into ax-2
10933→→¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒¬¬→𝜓¬⋀𝜒𝜃Modus ponens 10931, 10932
10934→¬𝜒¬¬→𝜓¬⋀𝜒𝜃Modus ponens 10897, 10933
10935→→¬𝜒¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-3
10936→¬→𝜓¬⋀𝜒𝜃𝜒Modus ponens 10934, 10935
10937→↔⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into biimp
10938→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 10849, 10937
10939→→¬→𝜓¬⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10940→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒Modus ponens 10936, 10939
10941→→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-2
10942→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 10940, 10941
10943→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 10938, 10942
10944→→𝜒→𝜑𝜒→⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10945→⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒Modus ponens 1834, 10944
10946→→⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒→→⋀𝜓⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
10947→→⋀𝜓⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→𝜑𝜒Modus ponens 10945, 10946
10948→⋀𝜓⋀𝜒𝜃→𝜑𝜒Modus ponens 10943, 10947
10949↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into df-an
10950→𝜑→⋀𝜓⋀𝜒𝜃𝜑Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10951→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑Subs [𝜑↗→𝜑→⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬¬𝜑] into ax-1
10952→¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑Modus ponens 10950, 10951
10953→→¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜑] into ax-2
10954→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑Modus ponens 10952, 10953
10955→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑Modus ponens notnotr, 10954
10956→→⋀𝜓⋀𝜒𝜃→𝜑𝜒→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-2
10957→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 10948, 10956
10958→→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗¬¬𝜑] into ax-1
10959→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 10957, 10958
10960→→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜒] into ax-2
10961→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 10959, 10960
10962→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 10955, 10961
10963→⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃] into id
10964→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬𝜑] into ax-1
10965→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10966→⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃Modus ponens 10964, 10965
10967→→⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→→⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑⋀𝜓⋀𝜒𝜃] into ax-2
10968→→⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃Modus ponens 10966, 10967
10969→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-2
10970→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒Modus ponens 10962, 10969
10971→→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒Subs [𝜑↗→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10972→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒Modus ponens 10970, 10971
10973→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑𝜒] into ax-2
10974→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒Modus ponens 10972, 10973
10975→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒Modus ponens 10964, 10974
10976→→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒Subs [𝜑↗→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10977→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒Modus ponens 9357, 10976
10978→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑𝜒, 𝜒↗→¬¬𝜑¬¬𝜒] into ax-2
10979→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒Modus ponens 10977, 10978
10980→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒Modus ponens 10975, 10979
10981→→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑Subs [𝜑↗→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10982→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑Modus ponens 9363, 10981
10983→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑¬¬𝜒, 𝜒↗→¬𝜒¬𝜑] into ax-2
10984→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑Modus ponens 10982, 10983
10985→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑Modus ponens 10980, 10984
10986→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10987→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒Subs [𝜑↗→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10988→¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒Modus ponens 10986, 10987
10989→→¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜒] into ax-2
10990→→¬𝜒¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒Modus ponens 10988, 10989
10991→→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬𝜑] into ax-2
10992→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 10985, 10991
10993→→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
10994→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 10992, 10993
10995→→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜒, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
10996→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 10994, 10995
10997→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 10986, 10996
10998→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into id
10999→→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
11000→¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 10998, 10999
11001→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into notnotr
11002→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
11003→→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11004→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11002, 11003
11005→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11006→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11004, 11005
11007→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11001, 11006
11008→→¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11009→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11000, 11008
11010→→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11011→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11009, 11010
11012→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11013→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11011, 11012
11014→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11015→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1
11016→¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒Modus ponens 11014, 11015
11017→→¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒] into ax-2
11018→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒Modus ponens 11016, 11017
11019→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11020→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11007, 11019
11021→→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
11022→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11020, 11021
11023→→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11024→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11022, 11023
11025→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11014, 11024
11026→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3
11027→→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
11028→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11026, 11027
11029→→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11030→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11028, 11029
11031→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11025, 11030
11032→→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11033→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11031, 11032
11034→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 10997, 11033
11035→→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3
11036→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒Modus ponens 11034, 11035
11037→↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into biimp
11038→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 10949, 11037
11039→→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-1
11040→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒Modus ponens 11036, 11039
11041→→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11042→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒Modus ponens 11040, 11041
11043→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒Modus ponens 11038, 11042
11044→↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into bicom1
11045↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑Modus ponens 10949, 11044
11046→↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into biimp
11047→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑Modus ponens 11045, 11046
11048→→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒Subs [𝜑↗→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11049→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒Modus ponens 11043, 11048
11050→→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-2
11051→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒Modus ponens 11049, 11050
11052→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into pm3.2im
11053→→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒, 𝜓↗𝜑] into ax-1
11054→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒Modus ponens 11036, 11053
11055→→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒Subs [𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11056→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒Modus ponens 11054, 11055
11057→→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒Subs [𝜑↗→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11058→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒Modus ponens 11056, 11057
11059→→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜒Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→𝜑𝜒] into ax-2
11060→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜒Modus ponens 11058, 11059
11061→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑Subs [𝜑↗→𝜑→⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
11062→𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑Modus ponens 10950, 11061
11063→→𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑Subs [𝜓↗𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜑] into ax-2
11064→→𝜑𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑Modus ponens 11062, 11063
11065→→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1
11066→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 10957, 11065
11067→→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜒Subs [𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜒] into ax-2
11068→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11066, 11067
11069→𝜑→⋀𝜓⋀𝜒𝜃𝜒Modus ponens 10950, 11068
11070↔⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into df-an
11071→¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃] into notnotr
11072→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1
11073→→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11074→¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃Modus ponens 11072, 11073
11075→→¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→→¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑⋀𝜓⋀𝜒𝜃] into ax-2
11076→→¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃Modus ponens 11074, 11075
11077→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃Modus ponens 11071, 11076
11078→→𝜑→⋀𝜓⋀𝜒𝜃𝜒→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into ax-2
11079→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒Modus ponens 11069, 11078
11080→→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒Subs [𝜑↗→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11081→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒Modus ponens 11079, 11080
11082→→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑𝜒] into ax-2
11083→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒Modus ponens 11081, 11082
11084→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒Modus ponens 11077, 11083
11085→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑Subs [𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11086→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑Subs [𝜑↗→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
11087→𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑Modus ponens 11085, 11086
11088→→𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→→𝜑𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜑] into ax-2
11089→→𝜑𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑Modus ponens 11087, 11088
11090→→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-2
11091→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11084, 11090
11092→→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1
11093→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11091, 11092
11094→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜒] into ax-2
11095→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11093, 11094
11096→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11085, 11095
11097→→𝜒¬¬𝜒→¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11098→¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒Modus ponens 9172, 11097
11099→→¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
11100→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒Modus ponens 11098, 11099
11101→→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒, 𝜓↗𝜑] into ax-1
11102→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒Modus ponens 11100, 11101
11103→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜒, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒] into ax-2
11104→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒Modus ponens 11102, 11103
11105→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒Modus ponens 11096, 11104
11106→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-3
11107→→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1
11108→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃Modus ponens 11106, 11107
11109→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜓⋀𝜒𝜃] into ax-2
11110→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃Modus ponens 11108, 11109
11111→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃Modus ponens 11105, 11110
11112→→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜓↗¬𝜒, 𝜒↗¬⋀𝜓⋀𝜒𝜃] into ax-2
11113→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11111, 11112
11114→→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11115→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11113, 11114
11116→→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11117→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11115, 11116
11118→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 9465, 11117
11119→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into id
11120→→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11121→¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11119, 11120
11122→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into notnotr
11123→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11124→→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11125→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11123, 11124
11126→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11127→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11125, 11126
11128→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11122, 11127
11129→→¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11130→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11121, 11129
11131→→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11132→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11130, 11131
11133→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11134→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11132, 11133
11135→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11136→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒Subs [𝜑↗→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
11137→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒Modus ponens 11135, 11136
11138→→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒] into ax-2
11139→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒Modus ponens 11137, 11138
11140→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11141→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11128, 11140
11142→→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11143→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11141, 11142
11144→→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11145→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11143, 11144
11146→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11135, 11145
11147→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3
11148→→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11149→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11147, 11148
11150→→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11151→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11149, 11150
11152→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11146, 11151
11153→→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11154→→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11152, 11153
11155→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11118, 11154
11156→→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3
11157→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11155, 11156
11158→↔⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into biimp
11159→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11070, 11158
11160→→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1
11161→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11157, 11160
11162→→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜒Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11163→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11161, 11162
11164→⋀𝜑⋀𝜓⋀𝜒𝜃𝜒Modus ponens 11159, 11163simprrl
11165→⋀𝜒𝜃𝜃Subs [𝜑↗𝜒, 𝜓↗𝜃] into simpr
11166→𝜃→𝜓𝜃Subs [𝜑↗𝜃] into ax-1
11167→→𝜃→𝜓𝜃→⋀𝜒𝜃→𝜃→𝜓𝜃Subs [𝜑↗→𝜃→𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11168→⋀𝜒𝜃→𝜃→𝜓𝜃Modus ponens 11166, 11167
11169→→⋀𝜒𝜃→𝜃→𝜓𝜃→→⋀𝜒𝜃𝜃→⋀𝜒𝜃→𝜓𝜃Subs [𝜑↗⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗→𝜓𝜃] into ax-2
11170→→⋀𝜒𝜃𝜃→⋀𝜒𝜃→𝜓𝜃Modus ponens 11168, 11169
11171→⋀𝜒𝜃→𝜓𝜃Modus ponens 11165, 11170
11172→→⋀𝜒𝜃→𝜓𝜃→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃Subs [𝜑↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11173→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃Modus ponens 11171, 11172
11174→→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃, 𝜓↗¬¬𝜓] into ax-1
11175→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃Modus ponens 11173, 11174
11176→→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜃Subs [𝜑↗¬¬𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜃] into ax-2
11177→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜃Modus ponens 11175, 11176
11178→¬¬𝜓→⋀𝜒𝜃𝜃Modus ponens 10734, 11177
11179→→¬¬𝜓→⋀𝜒𝜃𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11180→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃Modus ponens 11178, 11179
11181→→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃Subs [𝜑↗→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11182→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃Modus ponens 11180, 11181
11183→→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜃Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜓𝜃] into ax-2
11184→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜃Modus ponens 11182, 11183
11185→⋀𝜒𝜃→¬¬𝜓𝜃Modus ponens 10743, 11184
11186→𝜃¬¬𝜃Subs [𝜑↗𝜃] into notnot
11187→→𝜃¬¬𝜃→¬¬𝜓→𝜃¬¬𝜃Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬𝜓] into ax-1
11188→¬¬𝜓→𝜃¬¬𝜃Modus ponens 11186, 11187
11189→→¬¬𝜓→𝜃¬¬𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃Subs [𝜑↗¬¬𝜓, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2
11190→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃Modus ponens 11188, 11189
11191→→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃Subs [𝜑↗→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11192→⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃Modus ponens 11190, 11191
11193→→⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃→→⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→¬¬𝜓¬¬𝜃Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓𝜃, 𝜒↗→¬¬𝜓¬¬𝜃] into ax-2
11194→→⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→¬¬𝜓¬¬𝜃Modus ponens 11192, 11193
11195→⋀𝜒𝜃→¬¬𝜓¬¬𝜃Modus ponens 11185, 11194
11196→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜃] into ax-3
11197→→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓→⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-1
11198→⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓Modus ponens 11196, 11197
11199→→⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓→→⋀𝜒𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→¬𝜃¬𝜓Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓¬¬𝜃, 𝜒↗→¬𝜃¬𝜓] into ax-2
11200→→⋀𝜒𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→¬𝜃¬𝜓Modus ponens 11198, 11199
11201→⋀𝜒𝜃→¬𝜃¬𝜓Modus ponens 11195, 11200
11202→¬𝜃¬𝜃Subs [𝜑↗¬𝜃] into id
11203→¬𝜃→⋀𝜒𝜃¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11204→→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃Subs [𝜑↗→¬𝜃→⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1
11205→¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃Modus ponens 11203, 11204
11206→→¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→⋀𝜒𝜃¬𝜃] into ax-2
11207→→¬𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃Modus ponens 11205, 11206
11208→→⋀𝜒𝜃→¬𝜃¬𝜓→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬𝜓] into ax-2
11209→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓Modus ponens 11201, 11208
11210→→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓Subs [𝜑↗→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11211→¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓Modus ponens 11209, 11210
11212→→¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓→→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜒𝜃¬𝜃, 𝜒↗→⋀𝜒𝜃¬𝜓] into ax-2
11213→→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜓Modus ponens 11211, 11212
11214→¬𝜃→⋀𝜒𝜃¬𝜓Modus ponens 11203, 11213
11215→→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11216→¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 10777, 11215
11217→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11218→→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
11219→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Modus ponens 11217, 11218
11220→→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜃¬→⋀𝜒𝜃¬𝜓] into ax-2
11221→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Modus ponens 11219, 11220
11222→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Modus ponens 10780, 11221
11223→→¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2
11224→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Modus ponens 11216, 11223
11225→→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
11226→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Modus ponens 11224, 11225
11227→→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜃¬→⋀𝜒𝜃¬𝜓] into ax-2
11228→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓Modus ponens 11226, 11227
11229→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
11230→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃Subs [𝜑↗→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃, 𝜓↗¬𝜃] into ax-1
11231→¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃Modus ponens 11229, 11230
11232→→¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃] into ax-2
11233→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃Modus ponens 11231, 11232
11234→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2
11235→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 11222, 11234
11236→→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11237→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 11235, 11236
11238→→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓] into ax-2
11239→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 11237, 11238
11240→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓Modus ponens 11229, 11239
11241→→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11242→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Modus ponens 10805, 11241
11243→→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓] into ax-2
11244→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Modus ponens 11242, 11243
11245→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓Modus ponens 11240, 11244
11246→→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃¬¬→⋀𝜒𝜃¬𝜓Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜒𝜃¬𝜓, 𝜒↗¬¬→⋀𝜒𝜃¬𝜓] into ax-2
11247→→¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃¬¬→⋀𝜒𝜃¬𝜓Modus ponens 11245, 11246
11248→¬𝜃¬¬→⋀𝜒𝜃¬𝜓Modus ponens 11214, 11247
11249→→¬𝜃¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓𝜃Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-3
11250→¬→⋀𝜒𝜃¬𝜓𝜃Modus ponens 11248, 11249
11251→→¬→⋀𝜒𝜃¬𝜓𝜃→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜃, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-1
11252→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃Modus ponens 11250, 11251
11253→→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗𝜃] into ax-2
11254→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃Modus ponens 11252, 11253
11255→⋀⋀𝜒𝜃𝜓𝜃Modus ponens 10817, 11254
11256→→⋀⋀𝜒𝜃𝜓𝜃→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃Subs [𝜑↗→⋀⋀𝜒𝜃𝜓𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-1
11257→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃Modus ponens 11255, 11256
11258→→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓, 𝜒↗𝜃] into ax-2
11259→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃Modus ponens 11257, 11258
11260→→¬→⋀𝜒𝜃¬𝜓𝜃→𝜓→¬→⋀𝜒𝜃¬𝜓𝜃Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜃] into ax-1
11261→𝜓→¬→⋀𝜒𝜃¬𝜓𝜃Modus ponens 11250, 11260
11262→→𝜓→¬→⋀𝜒𝜃¬𝜓𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗𝜃] into ax-2
11263→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃Modus ponens 11261, 11262
11264→→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃Subs [𝜑↗→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11265→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃Modus ponens 11263, 11264
11266→→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜃Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→𝜓𝜃] into ax-2
11267→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜃Modus ponens 11265, 11266
11268→→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃] into ax-1
11269→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃Modus ponens 11173, 11268
11270→→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜃Subs [𝜑↗𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜃] into ax-2
11271→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜃Modus ponens 11269, 11270
11272→𝜓→⋀𝜒𝜃𝜃Modus ponens 10729, 11271
11273→→𝜓→⋀𝜒𝜃𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11274→→𝜓⋀𝜒𝜃→𝜓𝜃Modus ponens 11272, 11273
11275→→→𝜓⋀𝜒𝜃→𝜓𝜃→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃Subs [𝜑↗→→𝜓⋀𝜒𝜃→𝜓𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
11276→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃Modus ponens 11274, 11275
11277→→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜃Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗→𝜓⋀𝜒𝜃, 𝜒↗→𝜓𝜃] into ax-2
11278→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜃Modus ponens 11276, 11277
11279→¬¬⋀𝜒𝜃→𝜓𝜃Modus ponens 10856, 11278
11280→→¬¬⋀𝜒𝜃→𝜓𝜃→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11281→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃Modus ponens 11279, 11280
11282→→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃] into ax-1
11283→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃Modus ponens 11281, 11282
11284→→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜃Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜃] into ax-2
11285→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜃Modus ponens 11283, 11284
11286→𝜓→¬¬⋀𝜒𝜃𝜃Modus ponens 10864, 11285
11287→→𝜃¬¬𝜃→¬¬⋀𝜒𝜃→𝜃¬¬𝜃Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
11288→¬¬⋀𝜒𝜃→𝜃¬¬𝜃Modus ponens 11186, 11287
11289→→¬¬⋀𝜒𝜃→𝜃¬¬𝜃→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2
11290→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃Modus ponens 11288, 11289
11291→→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃] into ax-1
11292→𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃Modus ponens 11290, 11291
11293→→𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃→→𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→¬¬⋀𝜒𝜃¬¬𝜃Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜃, 𝜒↗→¬¬⋀𝜒𝜃¬¬𝜃] into ax-2
11294→→𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→¬¬⋀𝜒𝜃¬¬𝜃Modus ponens 11292, 11293
11295→𝜓→¬¬⋀𝜒𝜃¬¬𝜃Modus ponens 11286, 11294
11296→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃Subs [𝜑↗¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-3
11297→→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃→𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃Subs [𝜑↗→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃] into ax-1
11298→𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃Modus ponens 11296, 11297
11299→→𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃→→𝜓→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→¬𝜃¬⋀𝜒𝜃Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃¬¬𝜃, 𝜒↗→¬𝜃¬⋀𝜒𝜃] into ax-2
11300→→𝜓→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→¬𝜃¬⋀𝜒𝜃Modus ponens 11298, 11299
11301→𝜓→¬𝜃¬⋀𝜒𝜃Modus ponens 11295, 11300
11302→¬𝜃→𝜓¬𝜃Subs [𝜑↗¬𝜃] into ax-1
11303→→¬𝜃→𝜓¬𝜃→¬𝜃→¬𝜃→𝜓¬𝜃Subs [𝜑↗→¬𝜃→𝜓¬𝜃, 𝜓↗¬𝜃] into ax-1
11304→¬𝜃→¬𝜃→𝜓¬𝜃Modus ponens 11302, 11303
11305→→¬𝜃→¬𝜃→𝜓¬𝜃→→¬𝜃¬𝜃→¬𝜃→𝜓¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→𝜓¬𝜃] into ax-2
11306→→¬𝜃¬𝜃→¬𝜃→𝜓¬𝜃Modus ponens 11304, 11305
11307→→𝜓→¬𝜃¬⋀𝜒𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃Subs [𝜑↗𝜓, 𝜓↗¬𝜃, 𝜒↗¬⋀𝜒𝜃] into ax-2
11308→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃Modus ponens 11301, 11307
11309→→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃Subs [𝜑↗→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11310→¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃Modus ponens 11308, 11309
11311→→¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃→→¬𝜃→𝜓¬𝜃→¬𝜃→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗→𝜓¬𝜃, 𝜒↗→𝜓¬⋀𝜒𝜃] into ax-2
11312→→¬𝜃→𝜓¬𝜃→¬𝜃→𝜓¬⋀𝜒𝜃Modus ponens 11310, 11311
11313→¬𝜃→𝜓¬⋀𝜒𝜃Modus ponens 11302, 11312
11314→→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11315→¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 10898, 11314
11316→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11317→→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
11318→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11316, 11317
11319→→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2
11320→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11318, 11319
11321→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 10901, 11320
11322→→¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2
11323→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11315, 11322
11324→→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
11325→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11323, 11324
11326→→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2
11327→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11325, 11326
11328→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
11329→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃Subs [𝜑↗→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1
11330→¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃Modus ponens 11328, 11329
11331→→¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃] into ax-2
11332→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃Modus ponens 11330, 11331
11333→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2
11334→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11321, 11333
11335→→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11336→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11334, 11335
11337→→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2
11338→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11336, 11337
11339→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃Modus ponens 11328, 11338
11340→→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11341→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Modus ponens 10926, 11340
11342→→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃] into ax-2
11343→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Modus ponens 11341, 11342
11344→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃Modus ponens 11339, 11343
11345→→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃¬¬→𝜓¬⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗→𝜓¬⋀𝜒𝜃, 𝜒↗¬¬→𝜓¬⋀𝜒𝜃] into ax-2
11346→→¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃¬¬→𝜓¬⋀𝜒𝜃Modus ponens 11344, 11345
11347→¬𝜃¬¬→𝜓¬⋀𝜒𝜃Modus ponens 11313, 11346
11348→→¬𝜃¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃Subs [𝜑↗𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-3
11349→¬→𝜓¬⋀𝜒𝜃𝜃Modus ponens 11347, 11348
11350→→¬→𝜓¬⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11351→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃Modus ponens 11349, 11350
11352→→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11353→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11351, 11352
11354→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 10938, 11353
11355→𝜃→𝜑𝜃Subs [𝜑↗𝜃, 𝜓↗𝜑] into ax-1
11356→→𝜃→𝜑𝜃→⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃Subs [𝜑↗→𝜃→𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11357→⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃Modus ponens 11355, 11356
11358→→⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃→→⋀𝜓⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→𝜑𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗→𝜑𝜃] into ax-2
11359→→⋀𝜓⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→𝜑𝜃Modus ponens 11357, 11358
11360→⋀𝜓⋀𝜒𝜃→𝜑𝜃Modus ponens 11354, 11359
11361→→⋀𝜓⋀𝜒𝜃→𝜑𝜃→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜃] into ax-2
11362→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11360, 11361
11363→→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗¬¬𝜑] into ax-1
11364→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11362, 11363
11365→→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜃] into ax-2
11366→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11364, 11365
11367→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 10955, 11366
11368→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11369→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃Modus ponens 11367, 11368
11370→→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃Subs [𝜑↗→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11371→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃Modus ponens 11369, 11370
11372→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑𝜃] into ax-2
11373→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃Modus ponens 11371, 11372
11374→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃Modus ponens 10964, 11373
11375→→𝜃¬¬𝜃→¬¬𝜑→𝜃¬¬𝜃Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬𝜑] into ax-1
11376→¬¬𝜑→𝜃¬¬𝜃Modus ponens 11186, 11375
11377→→¬¬𝜑→𝜃¬¬𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃Subs [𝜑↗¬¬𝜑, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2
11378→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃Modus ponens 11376, 11377
11379→→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃Subs [𝜑↗→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11380→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃Modus ponens 11378, 11379
11381→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑𝜃, 𝜒↗→¬¬𝜑¬¬𝜃] into ax-2
11382→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃Modus ponens 11380, 11381
11383→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃Modus ponens 11374, 11382
11384→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜃] into ax-3
11385→→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑Subs [𝜑↗→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11386→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑Modus ponens 11384, 11385
11387→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑¬¬𝜃, 𝜒↗→¬𝜃¬𝜑] into ax-2
11388→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑Modus ponens 11386, 11387
11389→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑Modus ponens 11383, 11388
11390→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11391→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃Subs [𝜑↗→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1
11392→¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃Modus ponens 11390, 11391
11393→→¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜃] into ax-2
11394→→¬𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃Modus ponens 11392, 11393
11395→→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬𝜑] into ax-2
11396→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11389, 11395
11397→→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11398→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11396, 11397
11399→→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜃, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11400→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11398, 11399
11401→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11390, 11400
11402→→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11403→¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 10998, 11402
11404→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11405→→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11406→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11404, 11405
11407→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11408→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11406, 11407
11409→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11001, 11408
11410→→¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11411→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11403, 11410
11412→→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11413→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11411, 11412
11414→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11415→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11413, 11414
11416→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11417→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃Subs [𝜑↗→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃, 𝜓↗¬𝜃] into ax-1
11418→¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃Modus ponens 11416, 11417
11419→→¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃] into ax-2
11420→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃Modus ponens 11418, 11419
11421→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11422→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11409, 11421
11423→→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11424→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11422, 11423
11425→→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11426→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11424, 11425
11427→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11416, 11426
11428→→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11429→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11026, 11428
11430→→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11431→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11429, 11430
11432→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11427, 11431
11433→→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11434→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11432, 11433
11435→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑Modus ponens 11401, 11434
11436→→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3
11437→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃Modus ponens 11435, 11436
11438→→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-1
11439→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃Modus ponens 11437, 11438
11440→→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗𝜃] into ax-2
11441→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃Modus ponens 11439, 11440
11442→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃Modus ponens 11038, 11441
11443→→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃Subs [𝜑↗→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11444→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃Modus ponens 11442, 11443
11445→→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗𝜃] into ax-2
11446→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃Modus ponens 11444, 11445
11447→→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃, 𝜓↗𝜑] into ax-1
11448→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃Modus ponens 11437, 11447
11449→→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃Subs [𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗𝜃] into ax-2
11450→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃Modus ponens 11448, 11449
11451→→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃Subs [𝜑↗→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11452→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃Modus ponens 11450, 11451
11453→→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜃Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→𝜑𝜃] into ax-2
11454→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜃Modus ponens 11452, 11453
11455→→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗𝜑] into ax-1
11456→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11362, 11455
11457→→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜃Subs [𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜃] into ax-2
11458→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11456, 11457
11459→𝜑→⋀𝜓⋀𝜒𝜃𝜃Modus ponens 10950, 11458
11460→→𝜑→⋀𝜓⋀𝜒𝜃𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃Subs [𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11461→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃Modus ponens 11459, 11460
11462→→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃Subs [𝜑↗→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11463→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃Modus ponens 11461, 11462
11464→→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑𝜃] into ax-2
11465→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃Modus ponens 11463, 11464
11466→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃Modus ponens 11077, 11465
11467→→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜃] into ax-2
11468→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11466, 11467
11469→→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗𝜑] into ax-1
11470→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11468, 11469
11471→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜃] into ax-2
11472→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11470, 11471
11473→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11085, 11472
11474→→𝜃¬¬𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11475→¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃Modus ponens 11186, 11474
11476→→¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2
11477→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃Modus ponens 11475, 11476
11478→→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃, 𝜓↗𝜑] into ax-1
11479→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃Modus ponens 11477, 11478
11480→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜃, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃] into ax-2
11481→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃Modus ponens 11479, 11480
11482→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃Modus ponens 11473, 11481
11483→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-3
11484→→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1
11485→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃Modus ponens 11483, 11484
11486→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃, 𝜒↗→¬𝜃¬⋀𝜓⋀𝜒𝜃] into ax-2
11487→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃Modus ponens 11485, 11486
11488→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃Modus ponens 11482, 11487
11489→¬𝜃→𝜑¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗𝜑] into ax-1
11490→→¬𝜃→𝜑¬𝜃→¬𝜃→¬𝜃→𝜑¬𝜃Subs [𝜑↗→¬𝜃→𝜑¬𝜃, 𝜓↗¬𝜃] into ax-1
11491→¬𝜃→¬𝜃→𝜑¬𝜃Modus ponens 11489, 11490
11492→→¬𝜃→¬𝜃→𝜑¬𝜃→→¬𝜃¬𝜃→¬𝜃→𝜑¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→𝜑¬𝜃] into ax-2
11493→→¬𝜃¬𝜃→¬𝜃→𝜑¬𝜃Modus ponens 11491, 11492
11494→→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜓↗¬𝜃, 𝜒↗¬⋀𝜓⋀𝜒𝜃] into ax-2
11495→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11488, 11494
11496→→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11497→¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11495, 11496
11498→→¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→𝜑¬𝜃→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗→𝜑¬𝜃, 𝜒↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11499→→¬𝜃→𝜑¬𝜃→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11497, 11498
11500→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11489, 11499
11501→→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11502→¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11119, 11501
11503→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11504→→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11505→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11503, 11504
11506→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11507→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11505, 11506
11508→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11122, 11507
11509→→¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11510→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11502, 11509
11511→→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11512→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11510, 11511
11513→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11514→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11512, 11513
11515→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11516→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃Subs [𝜑↗→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1
11517→¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃Modus ponens 11515, 11516
11518→→¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃] into ax-2
11519→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃Modus ponens 11517, 11518
11520→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11521→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11508, 11520
11522→→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11523→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11521, 11522
11524→→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11525→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11523, 11524
11526→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11515, 11525
11527→→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11528→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11147, 11527
11529→→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11530→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11528, 11529
11531→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11526, 11530
11532→→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Subs [𝜑↗¬𝜃, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11533→→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11531, 11532
11534→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃Modus ponens 11500, 11533
11535→→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3
11536→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11534, 11535
11537→→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1
11538→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11536, 11537
11539→→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜃Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11540→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11538, 11539
11541→⋀𝜑⋀𝜓⋀𝜒𝜃𝜃Modus ponens 11159, 11540simprrr
11542→𝜑→𝜏𝜑Subs [𝜓↗𝜏] into ax-1
11543→→𝜑→𝜏𝜑→⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑Subs [𝜑↗→𝜑→𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11544→⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑Modus ponens 11542, 11543
11545→→⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜏𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜏𝜑] into ax-2
11546→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜏𝜑Modus ponens 11544, 11545
11547→⋀⋀𝜑𝜓𝜒→𝜏𝜑Modus ponens simpll, 11546
11548↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into df-an
11549→¬¬𝜏𝜏Subs [𝜑↗𝜏] into notnotr
11550→𝜏→⋀⋀𝜑𝜓𝜒𝜏Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11551→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏Subs [𝜑↗→𝜏→⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬¬𝜏] into ax-1
11552→¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏Modus ponens 11550, 11551
11553→→¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏Subs [𝜑↗¬¬𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜏] into ax-2
11554→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏Modus ponens 11552, 11553
11555→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏Modus ponens 11549, 11554
11556→→⋀⋀𝜑𝜓𝜒→𝜏𝜑→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏, 𝜒↗𝜑] into ax-2
11557→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 11547, 11556
11558→→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗¬¬𝜏] into ax-1
11559→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 11557, 11558
11560→→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2
11561→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 11559, 11560
11562→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 11555, 11561
11563→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜏] into ax-1
11564→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11565→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒Modus ponens 11563, 11564
11566→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏⋀⋀𝜑𝜓𝜒] into ax-2
11567→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒Modus ponens 11565, 11566
11568→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2
11569→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑Modus ponens 11562, 11568
11570→→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑Subs [𝜑↗→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11571→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑Modus ponens 11569, 11570
11572→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏𝜑] into ax-2
11573→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑Modus ponens 11571, 11572
11574→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑Modus ponens 11563, 11573
11575→→𝜑¬¬𝜑→¬¬𝜏→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜏] into ax-1
11576→¬¬𝜏→𝜑¬¬𝜑Modus ponens notnot, 11575
11577→→¬¬𝜏→𝜑¬¬𝜑→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑Subs [𝜑↗¬¬𝜏, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
11578→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑Modus ponens 11576, 11577
11579→→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑Subs [𝜑↗→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11580→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑Modus ponens 11578, 11579
11581→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏𝜑, 𝜒↗→¬¬𝜏¬¬𝜑] into ax-2
11582→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑Modus ponens 11580, 11581
11583→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑Modus ponens 11574, 11582
11584→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏Subs [𝜑↗¬𝜏, 𝜓↗¬𝜑] into ax-3
11585→→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏Subs [𝜑↗→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11586→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏Modus ponens 11584, 11585
11587→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏¬¬𝜑, 𝜒↗→¬𝜑¬𝜏] into ax-2
11588→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏Modus ponens 11586, 11587
11589→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏Modus ponens 11583, 11588
11590→→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬𝜏] into ax-2
11591→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11589, 11590
11592→→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11593→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11591, 11592
11594→→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11595→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11593, 11594
11596→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 9716, 11595
11597→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into id
11598→→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11599→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11597, 11598
11600→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into notnotr
11601→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11602→→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11603→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11601, 11602
11604→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11605→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11603, 11604
11606→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11600, 11605
11607→→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11608→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11599, 11607
11609→→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11610→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11608, 11609
11611→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11612→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11610, 11611
11613→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11614→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1
11615→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑Modus ponens 11613, 11614
11616→→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑] into ax-2
11617→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑Modus ponens 11615, 11616
11618→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11619→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11606, 11618
11620→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11621→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11619, 11620
11622→→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11623→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11621, 11622
11624→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11613, 11623
11625→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3
11626→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11627→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11625, 11626
11628→→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11629→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11627, 11628
11630→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11624, 11629
11631→→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11632→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11630, 11631
11633→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11596, 11632
11634→→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑Subs [𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3
11635→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑Modus ponens 11633, 11634
11636→↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into biimp
11637→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11548, 11636
11638→→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into ax-1
11639→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑Modus ponens 11635, 11638
11640→→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜑] into ax-2
11641→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑Modus ponens 11639, 11640
11642→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑Modus ponens 11637, 11641
11643→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into simpl
11644→↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into bicom1
11645↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏Modus ponens 11548, 11644
11646→↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into biimp
11647→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏Modus ponens 11645, 11646
11648→→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11649→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑Modus ponens 11642, 11648
11650→→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗𝜑] into ax-2
11651→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑Modus ponens 11649, 11650
11652→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into pm3.2im
11653→→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑, 𝜓↗𝜏] into ax-1
11654→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑Modus ponens 11635, 11653
11655→→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑Subs [𝜑↗𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜑] into ax-2
11656→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑Modus ponens 11654, 11655
11657→→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑Subs [𝜑↗→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11658→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑Modus ponens 11656, 11657
11659→→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→𝜏𝜑] into ax-2
11660→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜑Modus ponens 11658, 11659
11661→𝜏𝜏Subs [𝜑↗𝜏] into id
11662→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏Subs [𝜑↗→𝜏→⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗𝜏] into ax-1
11663→𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏Modus ponens 11550, 11662
11664→→𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏→→𝜏𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏Subs [𝜑↗𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜏] into ax-2
11665→→𝜏𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏Modus ponens 11663, 11664
11666→→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗𝜏] into ax-1
11667→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 11557, 11666
11668→→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜑Subs [𝜑↗𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2
11669→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 11667, 11668
11670→𝜏→⋀⋀𝜑𝜓𝜒𝜑Modus ponens 11550, 11669
11671→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into ax-1
11672→→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11673→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒Modus ponens 11671, 11672
11674→→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏⋀⋀𝜑𝜓𝜒] into ax-2
11675→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒Modus ponens 11673, 11674
11676→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒Modus ponens 11643, 11675
11677→→𝜏→⋀⋀𝜑𝜓𝜒𝜑→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2
11678→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑Modus ponens 11670, 11677
11679→→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑Subs [𝜑↗→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11680→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑Modus ponens 11678, 11679
11681→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜑] into ax-2
11682→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Modus ponens 11680, 11681
11683→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Modus ponens 11676, 11682
11684→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11685→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜏] into ax-1
11686→𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 11684, 11685
11687→→𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜏𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
11688→→𝜏𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 11686, 11687
11689→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏, 𝜒↗𝜑] into ax-2
11690→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 11683, 11689
11691→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗𝜏] into ax-1
11692→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 11690, 11691
11693→→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2
11694→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 11692, 11693
11695→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 11684, 11694
11696→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃] into id
11697→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into ax-1
11698→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11699→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 11697, 11698
11700→→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2
11701→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 11699, 11700
11702→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2
11703→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Modus ponens 11695, 11702
11704→→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Subs [𝜑↗→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11705→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Modus ponens 11703, 11704
11706→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜑] into ax-2
11707→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Modus ponens 11705, 11706
11708↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into df-an
11709→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜏] into ax-1
11710→¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 11684, 11709
11711→→¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗¬¬𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
11712→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 11710, 11711
11713→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 11549, 11712
11714→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜏] into ax-1
11715→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 11690, 11714
11716→→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2
11717→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 11715, 11716
11718→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 11713, 11717
11719→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜏] into ax-1
11720→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11721→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 11719, 11720
11722→→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2
11723→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 11721, 11722
11724→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2
11725→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑Modus ponens 11718, 11724
11726→→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑Subs [𝜑↗→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11727→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑Modus ponens 11725, 11726
11728→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏𝜑] into ax-2
11729→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑Modus ponens 11727, 11728
11730→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑Modus ponens 11719, 11729
11731→→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑Subs [𝜑↗→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11732→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑Modus ponens 11578, 11731
11733→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏𝜑, 𝜒↗→¬¬𝜏¬¬𝜑] into ax-2
11734→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑Modus ponens 11732, 11733
11735→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑Modus ponens 11730, 11734
11736→→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏Subs [𝜑↗→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11737→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏Modus ponens 11584, 11736
11738→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏¬¬𝜑, 𝜒↗→¬𝜑¬𝜏] into ax-2
11739→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏Modus ponens 11737, 11738
11740→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏Modus ponens 11735, 11739
11741→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11742→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1
11743→¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑Modus ponens 11741, 11742
11744→→¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑] into ax-2
11745→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑Modus ponens 11743, 11744
11746→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜑, 𝜒↗¬𝜏] into ax-2
11747→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11740, 11746
11748→→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11749→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11747, 11748
11750→→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11751→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11749, 11750
11752→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11741, 11751
11753→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into id
11754→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11755→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11753, 11754
11756→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into notnotr
11757→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11758→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11759→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11757, 11758
11760→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11761→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11759, 11760
11762→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11756, 11761
11763→→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11764→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11755, 11763
11765→→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11766→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11764, 11765
11767→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11768→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11766, 11767
11769→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11770→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1
11771→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑Modus ponens 11769, 11770
11772→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑] into ax-2
11773→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑Modus ponens 11771, 11772
11774→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11775→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11762, 11774
11776→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11777→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11775, 11776
11778→→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11779→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11777, 11778
11780→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11769, 11779
11781→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3
11782→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11783→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11781, 11782
11784→→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11785→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11783, 11784
11786→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11780, 11785
11787→→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11788→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11786, 11787
11789→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11752, 11788
11790→→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑Subs [𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3
11791→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑Modus ponens 11789, 11790
11792→↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into biimp
11793→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11708, 11792
11794→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
11795→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑Modus ponens 11791, 11794
11796→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗𝜑] into ax-2
11797→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 11795, 11796
11798→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 11793, 11797simp-4l
11799→𝜓→𝜏𝜓Subs [𝜑↗𝜓, 𝜓↗𝜏] into ax-1
11800→→𝜓→𝜏𝜓→⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓Subs [𝜑↗→𝜓→𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11801→⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓Modus ponens 11799, 11800
11802→→⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜏𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜓] into ax-2
11803→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜏𝜓Modus ponens 11801, 11802
11804→⋀⋀𝜑𝜓𝜒→𝜏𝜓Modus ponens simplr, 11803
11805→→⋀⋀𝜑𝜓𝜒→𝜏𝜓→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏, 𝜒↗𝜓] into ax-2
11806→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 11804, 11805
11807→→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗¬¬𝜏] into ax-1
11808→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 11806, 11807
11809→→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2
11810→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 11808, 11809
11811→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 11555, 11810
11812→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2
11813→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓Modus ponens 11811, 11812
11814→→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓Subs [𝜑↗→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11815→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓Modus ponens 11813, 11814
11816→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏𝜓] into ax-2
11817→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓Modus ponens 11815, 11816
11818→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓Modus ponens 11563, 11817
11819→→𝜓¬¬𝜓→¬¬𝜏→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜏] into ax-1
11820→¬¬𝜏→𝜓¬¬𝜓Modus ponens 448, 11819
11821→→¬¬𝜏→𝜓¬¬𝜓→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓Subs [𝜑↗¬¬𝜏, 𝜒↗¬¬𝜓] into ax-2
11822→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓Modus ponens 11820, 11821
11823→→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓Subs [𝜑↗→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11824→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓Modus ponens 11822, 11823
11825→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏𝜓, 𝜒↗→¬¬𝜏¬¬𝜓] into ax-2
11826→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓Modus ponens 11824, 11825
11827→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓Modus ponens 11818, 11826
11828→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏Subs [𝜑↗¬𝜏, 𝜓↗¬𝜓] into ax-3
11829→→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏Subs [𝜑↗→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11830→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏Modus ponens 11828, 11829
11831→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏¬¬𝜓, 𝜒↗→¬𝜓¬𝜏] into ax-2
11832→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏Modus ponens 11830, 11831
11833→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏Modus ponens 11827, 11832
11834→→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜏] into ax-2
11835→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11833, 11834
11836→→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11837→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11835, 11836
11838→→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11839→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11837, 11838
11840→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 9916, 11839
11841→→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11842→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11597, 11841
11843→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11844→→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11845→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11843, 11844
11846→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11847→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11845, 11846
11848→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11600, 11847
11849→→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11850→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11842, 11849
11851→→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11852→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11850, 11851
11853→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11854→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11852, 11853
11855→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11856→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1
11857→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓Modus ponens 11855, 11856
11858→→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓] into ax-2
11859→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓Modus ponens 11857, 11858
11860→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11861→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11848, 11860
11862→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11863→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11861, 11862
11864→→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11865→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11863, 11864
11866→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11855, 11865
11867→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11868→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11625, 11867
11869→→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11870→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11868, 11869
11871→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11866, 11870
11872→→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11873→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11871, 11872
11874→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏Modus ponens 11840, 11873
11875→→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3
11876→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓Modus ponens 11874, 11875
11877→→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into ax-1
11878→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓Modus ponens 11876, 11877
11879→→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜓] into ax-2
11880→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓Modus ponens 11878, 11879
11881→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓Modus ponens 11637, 11880
11882→→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11883→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓Modus ponens 11881, 11882
11884→→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗𝜓] into ax-2
11885→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓Modus ponens 11883, 11884
11886→→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓, 𝜓↗𝜏] into ax-1
11887→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓Modus ponens 11876, 11886
11888→→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓Subs [𝜑↗𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜓] into ax-2
11889→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓Modus ponens 11887, 11888
11890→→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓Subs [𝜑↗→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11891→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓Modus ponens 11889, 11890
11892→→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→𝜏𝜓] into ax-2
11893→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜓Modus ponens 11891, 11892
11894→→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗𝜏] into ax-1
11895→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 11806, 11894
11896→→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜓Subs [𝜑↗𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2
11897→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 11895, 11896
11898→𝜏→⋀⋀𝜑𝜓𝜒𝜓Modus ponens 11550, 11897
11899→→𝜏→⋀⋀𝜑𝜓𝜒𝜓→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2
11900→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓Modus ponens 11898, 11899
11901→→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓Subs [𝜑↗→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11902→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓Modus ponens 11900, 11901
11903→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜓] into ax-2
11904→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Modus ponens 11902, 11903
11905→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Modus ponens 11676, 11904
11906→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏, 𝜒↗𝜓] into ax-2
11907→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 11905, 11906
11908→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗𝜏] into ax-1
11909→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 11907, 11908
11910→→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2
11911→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 11909, 11910
11912→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 11684, 11911
11913→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
11914→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Modus ponens 11912, 11913
11915→→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Subs [𝜑↗→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11916→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Modus ponens 11914, 11915
11917→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜓] into ax-2
11918→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Modus ponens 11916, 11917
11919→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗¬¬𝜏] into ax-1
11920→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 11907, 11919
11921→→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2
11922→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 11920, 11921
11923→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 11713, 11922
11924→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
11925→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓Modus ponens 11923, 11924
11926→→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓Subs [𝜑↗→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11927→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓Modus ponens 11925, 11926
11928→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏𝜓] into ax-2
11929→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓Modus ponens 11927, 11928
11930→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓Modus ponens 11719, 11929
11931→→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓Subs [𝜑↗→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11932→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓Modus ponens 11822, 11931
11933→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏𝜓, 𝜒↗→¬¬𝜏¬¬𝜓] into ax-2
11934→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓Modus ponens 11932, 11933
11935→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓Modus ponens 11930, 11934
11936→→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏Subs [𝜑↗→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11937→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏Modus ponens 11828, 11936
11938→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏¬¬𝜓, 𝜒↗→¬𝜓¬𝜏] into ax-2
11939→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏Modus ponens 11937, 11938
11940→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏Modus ponens 11935, 11939
11941→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11942→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
11943→¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓Modus ponens 11941, 11942
11944→→¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓] into ax-2
11945→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓Modus ponens 11943, 11944
11946→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜓, 𝜒↗¬𝜏] into ax-2
11947→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11940, 11946
11948→→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11949→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11947, 11948
11950→→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11951→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11949, 11950
11952→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11941, 11951
11953→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11954→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11753, 11953
11955→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11956→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11957→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11955, 11956
11958→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11959→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11957, 11958
11960→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11756, 11959
11961→→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11962→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11954, 11961
11963→→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11964→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11962, 11963
11965→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11966→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11964, 11965
11967→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11968→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1
11969→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓Modus ponens 11967, 11968
11970→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓] into ax-2
11971→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓Modus ponens 11969, 11970
11972→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11973→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11960, 11972
11974→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11975→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11973, 11974
11976→→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11977→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11975, 11976
11978→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11967, 11977
11979→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11980→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11781, 11979
11981→→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11982→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11980, 11981
11983→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11978, 11982
11984→→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11985→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11983, 11984
11986→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏Modus ponens 11952, 11985
11987→→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3
11988→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓Modus ponens 11986, 11987
11989→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
11990→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓Modus ponens 11988, 11989
11991→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗𝜓] into ax-2
11992→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 11990, 11991
11993→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 11793, 11992simp-4r
11994→→𝜑→𝜃𝜑→⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑Subs [𝜑↗→𝜑→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11995→⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑Modus ponens 9518, 11994
11996→→⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜃𝜑Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜃𝜑] into ax-2
11997→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜃𝜑Modus ponens 11995, 11996
11998→𝜑→𝜂𝜑Subs [𝜓↗𝜂] into ax-1
11999→→𝜑→𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑Subs [𝜑↗→𝜑→𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12000→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑Modus ponens 11998, 11999
12001→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→𝜂𝜑] into ax-2
12002→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Modus ponens 12000, 12001
12003→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Modus ponens simplll, 12002
12004↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into df-an
12005→¬¬𝜂𝜂Subs [𝜑↗𝜂] into notnotr
12006→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12007→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Subs [𝜑↗→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬¬𝜂] into ax-1
12008→¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Modus ponens 12006, 12007
12009→→¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Subs [𝜑↗¬¬𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-2
12010→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Modus ponens 12008, 12009
12011→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Modus ponens 12005, 12010
12012→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂, 𝜒↗𝜑] into ax-2
12013→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 12003, 12012
12014→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜂] into ax-1
12015→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 12013, 12014
12016→→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2
12017→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 12015, 12016
12018→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 12011, 12017
12019→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜂] into ax-1
12020→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12021→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 12019, 12020
12022→→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2
12023→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 12021, 12022
12024→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2
12025→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑Modus ponens 12018, 12024
12026→→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑Subs [𝜑↗→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12027→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑Modus ponens 12025, 12026
12028→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂𝜑] into ax-2
12029→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑Modus ponens 12027, 12028
12030→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑Modus ponens 12019, 12029
12031→→𝜑¬¬𝜑→¬¬𝜂→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜂] into ax-1
12032→¬¬𝜂→𝜑¬¬𝜑Modus ponens notnot, 12031
12033→→¬¬𝜂→𝜑¬¬𝜑→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑Subs [𝜑↗¬¬𝜂, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
12034→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑Modus ponens 12032, 12033
12035→→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑Subs [𝜑↗→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12036→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑Modus ponens 12034, 12035
12037→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂𝜑, 𝜒↗→¬¬𝜂¬¬𝜑] into ax-2
12038→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑Modus ponens 12036, 12037
12039→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑Modus ponens 12030, 12038
12040→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂Subs [𝜑↗¬𝜂, 𝜓↗¬𝜑] into ax-3
12041→→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂Subs [𝜑↗→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12042→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂Modus ponens 12040, 12041
12043→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂¬¬𝜑, 𝜒↗→¬𝜑¬𝜂] into ax-2
12044→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂Modus ponens 12042, 12043
12045→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂Modus ponens 12039, 12044
12046→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜑, 𝜒↗¬𝜂] into ax-2
12047→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12045, 12046
12048→→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12049→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12047, 12048
12050→→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12051→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12049, 12050
12052→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 11741, 12051
12053→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into id
12054→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12055→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12053, 12054
12056→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into notnotr
12057→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12058→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12059→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12057, 12058
12060→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12061→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12059, 12060
12062→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12056, 12061
12063→→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12064→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12055, 12063
12065→→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12066→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12064, 12065
12067→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12068→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12066, 12067
12069→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12070→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1
12071→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑Modus ponens 12069, 12070
12072→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑] into ax-2
12073→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑Modus ponens 12071, 12072
12074→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12075→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12062, 12074
12076→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12077→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12075, 12076
12078→→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12079→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12077, 12078
12080→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12069, 12079
12081→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3
12082→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12083→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12081, 12082
12084→→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12085→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12083, 12084
12086→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12080, 12085
12087→→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12088→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12086, 12087
12089→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12052, 12088
12090→→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑Subs [𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3
12091→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑Modus ponens 12089, 12090
12092→↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into biimp
12093→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12004, 12092
12094→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-1
12095→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑Modus ponens 12091, 12094
12096→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜑] into ax-2
12097→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑Modus ponens 12095, 12096
12098→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑Modus ponens 12093, 12097
12099→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into simpl
12100→↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into bicom1
12101↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Modus ponens 12004, 12100
12102→↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into biimp
12103→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Modus ponens 12101, 12102
12104→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12105→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑Modus ponens 12098, 12104
12106→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗𝜑] into ax-2
12107→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑Modus ponens 12105, 12106
12108→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into pm3.2im
12109→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑, 𝜓↗𝜂] into ax-1
12110→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑Modus ponens 12091, 12109
12111→→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑Subs [𝜑↗𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜑] into ax-2
12112→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑Modus ponens 12110, 12111
12113→→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑Subs [𝜑↗→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12114→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑Modus ponens 12112, 12113
12115→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→𝜂𝜑] into ax-2
12116→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Modus ponens 12114, 12115
12117→𝜂𝜂Subs [𝜑↗𝜂] into id
12118→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Subs [𝜑↗→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗𝜂] into ax-1
12119→𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Modus ponens 12006, 12118
12120→→𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→→𝜂𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Subs [𝜑↗𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-2
12121→→𝜂𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂Modus ponens 12119, 12120
12122→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗𝜂] into ax-1
12123→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 12013, 12122
12124→→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2
12125→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 12123, 12124
12126→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑Modus ponens 12006, 12125
12127→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into ax-1
12128→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12129→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 12127, 12128
12130→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2
12131→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 12129, 12130
12132→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃Modus ponens 12099, 12131
12133→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2
12134→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Modus ponens 12126, 12133
12135→→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Subs [𝜑↗→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12136→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑Modus ponens 12134, 12135
12137→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜑] into ax-2
12138→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Modus ponens 12136, 12137
12139→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Modus ponens 12132, 12138
12140→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12141→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜂] into ax-1
12142→𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12140, 12141
12143→→𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜂𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12144→→𝜂𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12142, 12143
12145→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂, 𝜒↗𝜑] into ax-2
12146→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12139, 12145
12147→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗𝜂] into ax-1
12148→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12146, 12147
12149→→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2
12150→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12148, 12149
12151→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12140, 12150
12152→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into id
12153→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into ax-1
12154→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12155→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12153, 12154
12156→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
12157→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12155, 12156
12158→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2
12159→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Modus ponens 12151, 12158
12160→→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Subs [𝜑↗→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12161→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Modus ponens 12159, 12160
12162→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜑] into ax-2
12163→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Modus ponens 12161, 12162
12164↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into df-an
12165→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜂] into ax-1
12166→¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12140, 12165
12167→→¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗¬¬𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12168→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12166, 12167
12169→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12005, 12168
12170→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗¬¬𝜂] into ax-1
12171→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12146, 12170
12172→→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2
12173→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12171, 12172
12174→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12169, 12173
12175→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜂] into ax-1
12176→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12177→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12175, 12176
12178→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
12179→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12177, 12178
12180→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2
12181→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑Modus ponens 12174, 12180
12182→→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑Subs [𝜑↗→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12183→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑Modus ponens 12181, 12182
12184→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂𝜑] into ax-2
12185→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑Modus ponens 12183, 12184
12186→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑Modus ponens 12175, 12185
12187→→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑Subs [𝜑↗→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12188→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑Modus ponens 12034, 12187
12189→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂𝜑, 𝜒↗→¬¬𝜂¬¬𝜑] into ax-2
12190→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑Modus ponens 12188, 12189
12191→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑Modus ponens 12186, 12190
12192→→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂Subs [𝜑↗→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12193→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂Modus ponens 12040, 12192
12194→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂¬¬𝜑, 𝜒↗→¬𝜑¬𝜂] into ax-2
12195→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂Modus ponens 12193, 12194
12196→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂Modus ponens 12191, 12195
12197→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12198→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1
12199→¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑Modus ponens 12197, 12198
12200→→¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑] into ax-2
12201→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑Modus ponens 12199, 12200
12202→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜑, 𝜒↗¬𝜂] into ax-2
12203→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12196, 12202
12204→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12205→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12203, 12204
12206→→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12207→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12205, 12206
12208→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12197, 12207
12209→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into id
12210→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12211→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12209, 12210
12212→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into notnotr
12213→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12214→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12215→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12213, 12214
12216→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12217→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12215, 12216
12218→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12212, 12217
12219→→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12220→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12211, 12219
12221→→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12222→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12220, 12221
12223→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12224→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12222, 12223
12225→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12226→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1
12227→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑Modus ponens 12225, 12226
12228→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑] into ax-2
12229→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑Modus ponens 12227, 12228
12230→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12231→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12218, 12230
12232→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12233→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12231, 12232
12234→→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12235→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12233, 12234
12236→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12225, 12235
12237→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3
12238→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12239→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12237, 12238
12240→→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12241→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12239, 12240
12242→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12236, 12241
12243→→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12244→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12242, 12243
12245→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12208, 12244
12246→→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑Subs [𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3
12247→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑Modus ponens 12245, 12246
12248→↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into biimp
12249→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12164, 12248
12250→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12251→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑Modus ponens 12247, 12250
12252→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗𝜑] into ax-2
12253→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12251, 12252
12254→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12249, 12253simp-5l
12255→→𝜓→𝜃𝜓→⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
12256→⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓Modus ponens 9774, 12255
12257→→⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
12258→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓Modus ponens 12256, 12257
12259→𝜓→𝜂𝜓Subs [𝜑↗𝜓, 𝜓↗𝜂] into ax-1
12260→→𝜓→𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓Subs [𝜑↗→𝜓→𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12261→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓Modus ponens 12259, 12260
12262→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜓] into ax-2
12263→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Modus ponens 12261, 12262
12264→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Modus ponens simpllr, 12263
12265→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂, 𝜒↗𝜓] into ax-2
12266→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 12264, 12265
12267→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗¬¬𝜂] into ax-1
12268→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 12266, 12267
12269→→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2
12270→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 12268, 12269
12271→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 12011, 12270
12272→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
12273→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓Modus ponens 12271, 12272
12274→→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓Subs [𝜑↗→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12275→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓Modus ponens 12273, 12274
12276→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂𝜓] into ax-2
12277→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓Modus ponens 12275, 12276
12278→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓Modus ponens 12019, 12277
12279→→𝜓¬¬𝜓→¬¬𝜂→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜂] into ax-1
12280→¬¬𝜂→𝜓¬¬𝜓Modus ponens 448, 12279
12281→→¬¬𝜂→𝜓¬¬𝜓→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓Subs [𝜑↗¬¬𝜂, 𝜒↗¬¬𝜓] into ax-2
12282→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓Modus ponens 12280, 12281
12283→→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓Subs [𝜑↗→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12284→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓Modus ponens 12282, 12283
12285→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂𝜓, 𝜒↗→¬¬𝜂¬¬𝜓] into ax-2
12286→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓Modus ponens 12284, 12285
12287→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓Modus ponens 12278, 12286
12288→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂Subs [𝜑↗¬𝜂, 𝜓↗¬𝜓] into ax-3
12289→→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂Subs [𝜑↗→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12290→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂Modus ponens 12288, 12289
12291→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂¬¬𝜓, 𝜒↗→¬𝜓¬𝜂] into ax-2
12292→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂Modus ponens 12290, 12291
12293→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂Modus ponens 12287, 12292
12294→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜓, 𝜒↗¬𝜂] into ax-2
12295→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12293, 12294
12296→→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12297→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12295, 12296
12298→→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12299→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12297, 12298
12300→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 11941, 12299
12301→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12302→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12053, 12301
12303→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12304→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12305→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12303, 12304
12306→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12307→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12305, 12306
12308→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12056, 12307
12309→→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12310→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12302, 12309
12311→→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12312→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12310, 12311
12313→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12314→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12312, 12313
12315→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12316→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1
12317→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓Modus ponens 12315, 12316
12318→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓] into ax-2
12319→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓Modus ponens 12317, 12318
12320→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12321→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12308, 12320
12322→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12323→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12321, 12322
12324→→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12325→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12323, 12324
12326→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12315, 12325
12327→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12328→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12081, 12327
12329→→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12330→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12328, 12329
12331→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12326, 12330
12332→→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12333→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12331, 12332
12334→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂Modus ponens 12300, 12333
12335→→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3
12336→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓Modus ponens 12334, 12335
12337→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-1
12338→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓Modus ponens 12336, 12337
12339→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜓] into ax-2
12340→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓Modus ponens 12338, 12339
12341→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓Modus ponens 12093, 12340
12342→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12343→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓Modus ponens 12341, 12342
12344→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗𝜓] into ax-2
12345→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓Modus ponens 12343, 12344
12346→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓, 𝜓↗𝜂] into ax-1
12347→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓Modus ponens 12336, 12346
12348→→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓Subs [𝜑↗𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜓] into ax-2
12349→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓Modus ponens 12347, 12348
12350→→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓Subs [𝜑↗→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12351→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓Modus ponens 12349, 12350
12352→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→𝜂𝜓] into ax-2
12353→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Modus ponens 12351, 12352
12354→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗𝜂] into ax-1
12355→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 12266, 12354
12356→→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2
12357→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 12355, 12356
12358→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓Modus ponens 12006, 12357
12359→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
12360→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Modus ponens 12358, 12359
12361→→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Subs [𝜑↗→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12362→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓Modus ponens 12360, 12361
12363→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜓] into ax-2
12364→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Modus ponens 12362, 12363
12365→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Modus ponens 12132, 12364
12366→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂, 𝜒↗𝜓] into ax-2
12367→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12365, 12366
12368→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗𝜂] into ax-1
12369→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12367, 12368
12370→→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2
12371→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12369, 12370
12372→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12140, 12371
12373→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2
12374→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Modus ponens 12372, 12373
12375→→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Subs [𝜑↗→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12376→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Modus ponens 12374, 12375
12377→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜓] into ax-2
12378→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Modus ponens 12376, 12377
12379→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗¬¬𝜂] into ax-1
12380→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12367, 12379
12381→→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2
12382→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12380, 12381
12383→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12169, 12382
12384→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2
12385→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓Modus ponens 12383, 12384
12386→→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓Subs [𝜑↗→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12387→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓Modus ponens 12385, 12386
12388→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂𝜓] into ax-2
12389→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓Modus ponens 12387, 12388
12390→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓Modus ponens 12175, 12389
12391→→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓Subs [𝜑↗→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12392→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓Modus ponens 12282, 12391
12393→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂𝜓, 𝜒↗→¬¬𝜂¬¬𝜓] into ax-2
12394→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓Modus ponens 12392, 12393
12395→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓Modus ponens 12390, 12394
12396→→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂Subs [𝜑↗→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12397→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂Modus ponens 12288, 12396
12398→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂¬¬𝜓, 𝜒↗→¬𝜓¬𝜂] into ax-2
12399→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂Modus ponens 12397, 12398
12400→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂Modus ponens 12395, 12399
12401→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12402→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1
12403→¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓Modus ponens 12401, 12402
12404→→¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓] into ax-2
12405→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓Modus ponens 12403, 12404
12406→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜓, 𝜒↗¬𝜂] into ax-2
12407→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12400, 12406
12408→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12409→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12407, 12408
12410→→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12411→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12409, 12410
12412→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12401, 12411
12413→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12414→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12209, 12413
12415→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12416→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12417→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12415, 12416
12418→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12419→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12417, 12418
12420→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12212, 12419
12421→→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12422→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12414, 12421
12423→→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12424→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12422, 12423
12425→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12426→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12424, 12425
12427→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12428→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1
12429→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓Modus ponens 12427, 12428
12430→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓] into ax-2
12431→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓Modus ponens 12429, 12430
12432→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12433→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12420, 12432
12434→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12435→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12433, 12434
12436→→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12437→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12435, 12436
12438→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12427, 12437
12439→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12440→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12237, 12439
12441→→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12442→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12440, 12441
12443→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12438, 12442
12444→→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12445→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12443, 12444
12446→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂Modus ponens 12412, 12445
12447→→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3
12448→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓Modus ponens 12446, 12447
12449→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12450→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓Modus ponens 12448, 12449
12451→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗𝜓] into ax-2
12452→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12450, 12451
12453→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12249, 12452simp-5r
12454→→𝜑→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑Subs [𝜑↗→𝜑→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12455→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑Modus ponens 11542, 12454
12456→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→𝜏𝜑] into ax-2
12457→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑Modus ponens 12455, 12456
12458→𝜑→𝜁𝜑Subs [𝜓↗𝜁] into ax-1
12459→→𝜑→𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑Subs [𝜑↗→𝜑→𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12460→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑Modus ponens 12458, 12459
12461→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜑, 𝜒↗→𝜁𝜑] into ax-2
12462→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Modus ponens 12460, 12461
12463→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Modus ponens simp-4l, 12462
12464↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into df-an
12465→¬¬𝜁𝜁Subs [𝜑↗𝜁] into notnotr
12466→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12467→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Subs [𝜑↗→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬¬𝜁] into ax-1
12468→¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Modus ponens 12466, 12467
12469→→¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Subs [𝜑↗¬¬𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-2
12470→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Modus ponens 12468, 12469
12471→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Modus ponens 12465, 12470
12472→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁, 𝜒↗𝜑] into ax-2
12473→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12463, 12472
12474→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗¬¬𝜁] into ax-1
12475→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12473, 12474
12476→→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2
12477→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12475, 12476
12478→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12471, 12477
12479→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜁] into ax-1
12480→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12481→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12479, 12480
12482→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
12483→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12481, 12482
12484→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2
12485→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑Modus ponens 12478, 12484
12486→→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12487→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑Modus ponens 12485, 12486
12488→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁𝜑] into ax-2
12489→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑Modus ponens 12487, 12488
12490→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑Modus ponens 12479, 12489
12491→→𝜑¬¬𝜑→¬¬𝜁→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜁] into ax-1
12492→¬¬𝜁→𝜑¬¬𝜑Modus ponens notnot, 12491
12493→→¬¬𝜁→𝜑¬¬𝜑→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑Subs [𝜑↗¬¬𝜁, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
12494→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑Modus ponens 12492, 12493
12495→→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑Subs [𝜑↗→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12496→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑Modus ponens 12494, 12495
12497→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁𝜑, 𝜒↗→¬¬𝜁¬¬𝜑] into ax-2
12498→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑Modus ponens 12496, 12497
12499→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑Modus ponens 12490, 12498
12500→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁Subs [𝜑↗¬𝜁, 𝜓↗¬𝜑] into ax-3
12501→→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁Subs [𝜑↗→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12502→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁Modus ponens 12500, 12501
12503→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁¬¬𝜑, 𝜒↗→¬𝜑¬𝜁] into ax-2
12504→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁Modus ponens 12502, 12503
12505→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁Modus ponens 12499, 12504
12506→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜑, 𝜒↗¬𝜁] into ax-2
12507→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12505, 12506
12508→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12509→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12507, 12508
12510→→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12511→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12509, 12510
12512→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12197, 12511
12513→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into id
12514→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12515→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12513, 12514
12516→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into notnotr
12517→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12518→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12519→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12517, 12518
12520→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12521→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12519, 12520
12522→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12516, 12521
12523→→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12524→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12515, 12523
12525→→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12526→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12524, 12525
12527→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12528→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12526, 12527
12529→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12530→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1
12531→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑Modus ponens 12529, 12530
12532→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑] into ax-2
12533→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑Modus ponens 12531, 12532
12534→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12535→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12522, 12534
12536→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12537→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12535, 12536
12538→→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12539→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12537, 12538
12540→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12529, 12539
12541→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3
12542→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12543→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12541, 12542
12544→→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12545→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12543, 12544
12546→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12540, 12545
12547→→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12548→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12546, 12547
12549→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12512, 12548
12550→→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑Subs [𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3
12551→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑Modus ponens 12549, 12550
12552→↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into biimp
12553→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12464, 12552
12554→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-1
12555→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑Modus ponens 12551, 12554
12556→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜑] into ax-2
12557→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑Modus ponens 12555, 12556
12558→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑Modus ponens 12553, 12557
12559→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into simpl
12560→↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into bicom1
12561↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Modus ponens 12464, 12560
12562→↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into biimp
12563→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Modus ponens 12561, 12562
12564→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12565→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑Modus ponens 12558, 12564
12566→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗𝜑] into ax-2
12567→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑Modus ponens 12565, 12566
12568→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into pm3.2im
12569→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑, 𝜓↗𝜁] into ax-1
12570→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑Modus ponens 12551, 12569
12571→→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑Subs [𝜑↗𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜑] into ax-2
12572→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑Modus ponens 12570, 12571
12573→→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑Subs [𝜑↗→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12574→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑Modus ponens 12572, 12573
12575→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→𝜁𝜑] into ax-2
12576→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Modus ponens 12574, 12575
12577→𝜁𝜁Subs [𝜑↗𝜁] into id
12578→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Subs [𝜑↗→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗𝜁] into ax-1
12579→𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Modus ponens 12466, 12578
12580→→𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→→𝜁𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Subs [𝜑↗𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-2
12581→→𝜁𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁Modus ponens 12579, 12580
12582→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗𝜁] into ax-1
12583→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12473, 12582
12584→→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2
12585→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12583, 12584
12586→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑Modus ponens 12466, 12585
12587→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into ax-1
12588→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12589→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12587, 12588
12590→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
12591→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12589, 12590
12592→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏Modus ponens 12559, 12591
12593→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2
12594→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Modus ponens 12586, 12593
12595→→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Subs [𝜑↗→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12596→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑Modus ponens 12594, 12595
12597→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜑] into ax-2
12598→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Modus ponens 12596, 12597
12599→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Modus ponens 12592, 12598
12600→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12601→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜁] into ax-1
12602→𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 12600, 12601
12603→→𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜁𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
12604→→𝜁𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 12602, 12603
12605→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁, 𝜒↗𝜑] into ax-2
12606→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12599, 12605
12607→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗𝜁] into ax-1
12608→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12606, 12607
12609→→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2
12610→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12608, 12609
12611→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12600, 12610
12612→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into id
12613→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into ax-1
12614→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12615→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12613, 12614
12616→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12617→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12615, 12616
12618→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2
12619→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Modus ponens 12611, 12618
12620→→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Subs [𝜑↗→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12621→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Modus ponens 12619, 12620
12622→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜑] into ax-2
12623→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Modus ponens 12621, 12622
12624↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into df-an
12625→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜁] into ax-1
12626→¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 12600, 12625
12627→→¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗¬¬𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
12628→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 12626, 12627
12629→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 12465, 12628
12630→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗¬¬𝜁] into ax-1
12631→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12606, 12630
12632→→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2
12633→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12631, 12632
12634→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12629, 12633
12635→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜁] into ax-1
12636→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12637→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12635, 12636
12638→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12639→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12637, 12638
12640→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2
12641→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑Modus ponens 12634, 12640
12642→→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12643→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑Modus ponens 12641, 12642
12644→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁𝜑] into ax-2
12645→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑Modus ponens 12643, 12644
12646→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑Modus ponens 12635, 12645
12647→→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑Subs [𝜑↗→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12648→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑Modus ponens 12494, 12647
12649→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁𝜑, 𝜒↗→¬¬𝜁¬¬𝜑] into ax-2
12650→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑Modus ponens 12648, 12649
12651→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑Modus ponens 12646, 12650
12652→→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁Subs [𝜑↗→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12653→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁Modus ponens 12500, 12652
12654→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁¬¬𝜑, 𝜒↗→¬𝜑¬𝜁] into ax-2
12655→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁Modus ponens 12653, 12654
12656→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁Modus ponens 12651, 12655
12657→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12658→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1
12659→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑Modus ponens 12657, 12658
12660→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑] into ax-2
12661→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑Modus ponens 12659, 12660
12662→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜑, 𝜒↗¬𝜁] into ax-2
12663→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12656, 12662
12664→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12665→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12663, 12664
12666→→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12667→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12665, 12666
12668→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12657, 12667
12669→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into id
12670→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12671→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12669, 12670
12672→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into notnotr
12673→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12674→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12675→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12673, 12674
12676→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12677→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12675, 12676
12678→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12672, 12677
12679→→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12680→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12671, 12679
12681→→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12682→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12680, 12681
12683→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12684→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12682, 12683
12685→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12686→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1
12687→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑Modus ponens 12685, 12686
12688→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑] into ax-2
12689→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑Modus ponens 12687, 12688
12690→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12691→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12678, 12690
12692→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12693→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12691, 12692
12694→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12695→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12693, 12694
12696→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12685, 12695
12697→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3
12698→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12699→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12697, 12698
12700→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12701→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12699, 12700
12702→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12696, 12701
12703→→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12704→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12702, 12703
12705→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12668, 12704
12706→→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3
12707→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑Modus ponens 12705, 12706
12708→↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into biimp
12709→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12624, 12708
12710→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
12711→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑Modus ponens 12707, 12710
12712→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗𝜑] into ax-2
12713→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 12711, 12712
12714→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 12709, 12713simp-6l
12715→→𝜓→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓Subs [𝜑↗→𝜓→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12716→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓Modus ponens 11799, 12715
12717→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜓] into ax-2
12718→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓Modus ponens 12716, 12717
12719→𝜓→𝜁𝜓Subs [𝜑↗𝜓, 𝜓↗𝜁] into ax-1
12720→→𝜓→𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓Subs [𝜑↗→𝜓→𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12721→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓Modus ponens 12719, 12720
12722→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜓] into ax-2
12723→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Modus ponens 12721, 12722
12724→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Modus ponens simp-4r, 12723
12725→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁, 𝜒↗𝜓] into ax-2
12726→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12724, 12725
12727→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗¬¬𝜁] into ax-1
12728→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12726, 12727
12729→→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2
12730→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12728, 12729
12731→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12471, 12730
12732→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2
12733→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓Modus ponens 12731, 12732
12734→→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12735→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓Modus ponens 12733, 12734
12736→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁𝜓] into ax-2
12737→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓Modus ponens 12735, 12736
12738→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓Modus ponens 12479, 12737
12739→→𝜓¬¬𝜓→¬¬𝜁→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜁] into ax-1
12740→¬¬𝜁→𝜓¬¬𝜓Modus ponens 448, 12739
12741→→¬¬𝜁→𝜓¬¬𝜓→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓Subs [𝜑↗¬¬𝜁, 𝜒↗¬¬𝜓] into ax-2
12742→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓Modus ponens 12740, 12741
12743→→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓Subs [𝜑↗→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12744→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓Modus ponens 12742, 12743
12745→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁𝜓, 𝜒↗→¬¬𝜁¬¬𝜓] into ax-2
12746→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓Modus ponens 12744, 12745
12747→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓Modus ponens 12738, 12746
12748→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁Subs [𝜑↗¬𝜁, 𝜓↗¬𝜓] into ax-3
12749→→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁Subs [𝜑↗→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12750→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁Modus ponens 12748, 12749
12751→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁¬¬𝜓, 𝜒↗→¬𝜓¬𝜁] into ax-2
12752→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁Modus ponens 12750, 12751
12753→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁Modus ponens 12747, 12752
12754→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜓, 𝜒↗¬𝜁] into ax-2
12755→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12753, 12754
12756→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12757→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12755, 12756
12758→→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12759→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12757, 12758
12760→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12401, 12759
12761→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12762→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12513, 12761
12763→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12764→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12765→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12763, 12764
12766→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12767→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12765, 12766
12768→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12516, 12767
12769→→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12770→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12762, 12769
12771→→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12772→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12770, 12771
12773→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12774→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12772, 12773
12775→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12776→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1
12777→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓Modus ponens 12775, 12776
12778→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓] into ax-2
12779→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓Modus ponens 12777, 12778
12780→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12781→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12768, 12780
12782→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12783→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12781, 12782
12784→→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12785→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12783, 12784
12786→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12775, 12785
12787→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12788→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12541, 12787
12789→→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12790→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12788, 12789
12791→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12786, 12790
12792→→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12793→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12791, 12792
12794→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁Modus ponens 12760, 12793
12795→→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3
12796→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓Modus ponens 12794, 12795
12797→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-1
12798→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓Modus ponens 12796, 12797
12799→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜓] into ax-2
12800→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓Modus ponens 12798, 12799
12801→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓Modus ponens 12553, 12800
12802→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12803→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓Modus ponens 12801, 12802
12804→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗𝜓] into ax-2
12805→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓Modus ponens 12803, 12804
12806→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓, 𝜓↗𝜁] into ax-1
12807→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓Modus ponens 12796, 12806
12808→→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓Subs [𝜑↗𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜓] into ax-2
12809→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓Modus ponens 12807, 12808
12810→→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓Subs [𝜑↗→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12811→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓Modus ponens 12809, 12810
12812→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→𝜁𝜓] into ax-2
12813→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Modus ponens 12811, 12812
12814→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗𝜁] into ax-1
12815→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12726, 12814
12816→→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2
12817→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12815, 12816
12818→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓Modus ponens 12466, 12817
12819→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2
12820→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Modus ponens 12818, 12819
12821→→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Subs [𝜑↗→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12822→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓Modus ponens 12820, 12821
12823→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜓] into ax-2
12824→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Modus ponens 12822, 12823
12825→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Modus ponens 12592, 12824
12826→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁, 𝜒↗𝜓] into ax-2
12827→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12825, 12826
12828→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗𝜁] into ax-1
12829→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12827, 12828
12830→→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2
12831→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12829, 12830
12832→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12600, 12831
12833→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2
12834→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Modus ponens 12832, 12833
12835→→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Subs [𝜑↗→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12836→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Modus ponens 12834, 12835
12837→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜓] into ax-2
12838→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Modus ponens 12836, 12837
12839→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗¬¬𝜁] into ax-1
12840→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12827, 12839
12841→→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2
12842→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12840, 12841
12843→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12629, 12842
12844→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2
12845→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓Modus ponens 12843, 12844
12846→→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12847→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓Modus ponens 12845, 12846
12848→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁𝜓] into ax-2
12849→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓Modus ponens 12847, 12848
12850→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓Modus ponens 12635, 12849
12851→→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓Subs [𝜑↗→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12852→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓Modus ponens 12742, 12851
12853→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁𝜓, 𝜒↗→¬¬𝜁¬¬𝜓] into ax-2
12854→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓Modus ponens 12852, 12853
12855→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓Modus ponens 12850, 12854
12856→→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁Subs [𝜑↗→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12857→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁Modus ponens 12748, 12856
12858→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁¬¬𝜓, 𝜒↗→¬𝜓¬𝜁] into ax-2
12859→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁Modus ponens 12857, 12858
12860→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁Modus ponens 12855, 12859
12861→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12862→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1
12863→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓Modus ponens 12861, 12862
12864→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓] into ax-2
12865→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓Modus ponens 12863, 12864
12866→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜓, 𝜒↗¬𝜁] into ax-2
12867→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12860, 12866
12868→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12869→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12867, 12868
12870→→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12871→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12869, 12870
12872→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12861, 12871
12873→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12874→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12669, 12873
12875→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12876→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12877→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12875, 12876
12878→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12879→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12877, 12878
12880→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12672, 12879
12881→→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12882→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12874, 12881
12883→→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12884→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12882, 12883
12885→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12886→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12884, 12885
12887→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12888→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1
12889→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓Modus ponens 12887, 12888
12890→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓] into ax-2
12891→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓Modus ponens 12889, 12890
12892→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12893→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12880, 12892
12894→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12895→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12893, 12894
12896→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12897→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12895, 12896
12898→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12887, 12897
12899→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12900→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12697, 12899
12901→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12902→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12900, 12901
12903→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12898, 12902
12904→→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12905→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12903, 12904
12906→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁Modus ponens 12872, 12905
12907→→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3
12908→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓Modus ponens 12906, 12907
12909→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
12910→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓Modus ponens 12908, 12909
12911→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗𝜓] into ax-2
12912→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 12910, 12911
12913→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 12709, 12912simp-6r
12914→→𝜑→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑Subs [𝜑↗→𝜑→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12915→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑Modus ponens 11998, 12914
12916→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜑, 𝜒↗→𝜂𝜑] into ax-2
12917→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑Modus ponens 12915, 12916
12918→𝜑→𝜎𝜑Subs [𝜓↗𝜎] into ax-1
12919→→𝜑→𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑Subs [𝜑↗→𝜑→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12920→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑Modus ponens 12918, 12919
12921→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜑, 𝜒↗→𝜎𝜑] into ax-2
12922→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Modus ponens 12920, 12921
12923→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Modus ponens simp-5l, 12922
12924↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into df-an
12925→¬¬𝜎𝜎Subs [𝜑↗𝜎] into notnotr
12926→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12927→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬¬𝜎] into ax-1
12928→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Modus ponens 12926, 12927
12929→→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Subs [𝜑↗¬¬𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-2
12930→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Modus ponens 12928, 12929
12931→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Modus ponens 12925, 12930
12932→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎, 𝜒↗𝜑] into ax-2
12933→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12923, 12932
12934→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗¬¬𝜎] into ax-1
12935→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12933, 12934
12936→→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2
12937→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12935, 12936
12938→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12931, 12937
12939→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜎] into ax-1
12940→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12941→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12939, 12940
12942→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12943→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 12941, 12942
12944→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2
12945→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑Modus ponens 12938, 12944
12946→→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12947→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑Modus ponens 12945, 12946
12948→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎𝜑] into ax-2
12949→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑Modus ponens 12947, 12948
12950→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑Modus ponens 12939, 12949
12951→→𝜑¬¬𝜑→¬¬𝜎→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜎] into ax-1
12952→¬¬𝜎→𝜑¬¬𝜑Modus ponens notnot, 12951
12953→→¬¬𝜎→𝜑¬¬𝜑→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑Subs [𝜑↗¬¬𝜎, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
12954→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑Modus ponens 12952, 12953
12955→→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑Subs [𝜑↗→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12956→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑Modus ponens 12954, 12955
12957→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎𝜑, 𝜒↗→¬¬𝜎¬¬𝜑] into ax-2
12958→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑Modus ponens 12956, 12957
12959→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑Modus ponens 12950, 12958
12960→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎Subs [𝜑↗¬𝜎, 𝜓↗¬𝜑] into ax-3
12961→→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎Subs [𝜑↗→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12962→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎Modus ponens 12960, 12961
12963→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎¬¬𝜑, 𝜒↗→¬𝜑¬𝜎] into ax-2
12964→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎Modus ponens 12962, 12963
12965→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎Modus ponens 12959, 12964
12966→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜑, 𝜒↗¬𝜎] into ax-2
12967→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12965, 12966
12968→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
12969→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12967, 12968
12970→→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12971→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12969, 12970
12972→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12657, 12971
12973→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into id
12974→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
12975→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12973, 12974
12976→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into notnotr
12977→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
12978→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
12979→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12977, 12978
12980→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12981→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12979, 12980
12982→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12976, 12981
12983→→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12984→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12975, 12983
12985→→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
12986→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12984, 12985
12987→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12988→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12986, 12987
12989→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
12990→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1
12991→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑Modus ponens 12989, 12990
12992→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑] into ax-2
12993→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑Modus ponens 12991, 12992
12994→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12995→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12982, 12994
12996→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
12997→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12995, 12996
12998→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12999→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12997, 12998
13000→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12989, 12999
13001→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3
13002→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
13003→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13001, 13002
13004→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13005→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13003, 13004
13006→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13000, 13005
13007→→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13008→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13006, 13007
13009→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12972, 13008
13010→→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3
13011→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑Modus ponens 13009, 13010
13012→↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into biimp
13013→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12924, 13012
13014→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-1
13015→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑Modus ponens 13011, 13014
13016→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜑] into ax-2
13017→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑Modus ponens 13015, 13016
13018→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑Modus ponens 13013, 13017
13019→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into simpl
13020→↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into bicom1
13021↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Modus ponens 12924, 13020
13022→↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into biimp
13023→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Modus ponens 13021, 13022
13024→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13025→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑Modus ponens 13018, 13024
13026→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗𝜑] into ax-2
13027→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑Modus ponens 13025, 13026
13028→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into pm3.2im
13029→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑, 𝜓↗𝜎] into ax-1
13030→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑Modus ponens 13011, 13029
13031→→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑Subs [𝜑↗𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜑] into ax-2
13032→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑Modus ponens 13030, 13031
13033→→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑Subs [𝜑↗→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13034→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑Modus ponens 13032, 13033
13035→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→𝜎𝜑] into ax-2
13036→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Modus ponens 13034, 13035
13037→𝜎𝜎Subs [𝜑↗𝜎] into id
13038→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗𝜎] into ax-1
13039→𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Modus ponens 12926, 13038
13040→→𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Subs [𝜑↗𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-2
13041→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎Modus ponens 13039, 13040
13042→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗𝜎] into ax-1
13043→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12933, 13042
13044→→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2
13045→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 13043, 13044
13046→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑Modus ponens 12926, 13045
13047→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into ax-1
13048→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13049→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 13047, 13048
13050→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
13051→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 13049, 13050
13052→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂Modus ponens 13019, 13051
13053→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2
13054→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Modus ponens 13046, 13053
13055→→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13056→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑Modus ponens 13054, 13055
13057→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜑] into ax-2
13058→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Modus ponens 13056, 13057
13059→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Modus ponens 13052, 13058
13060→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13061→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜎] into ax-1
13062→𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13060, 13061
13063→→𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13064→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13062, 13063
13065→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎, 𝜒↗𝜑] into ax-2
13066→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13059, 13065
13067→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗𝜎] into ax-1
13068→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13066, 13067
13069→→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2
13070→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13068, 13069
13071→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13060, 13070
13072→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into id
13073→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into ax-1
13074→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13075→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13073, 13074
13076→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
13077→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13075, 13076
13078→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2
13079→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Modus ponens 13071, 13078
13080→→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13081→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Modus ponens 13079, 13080
13082→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜑] into ax-2
13083→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Modus ponens 13081, 13082
13084↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into df-an
13085→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜎] into ax-1
13086→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13060, 13085
13087→→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗¬¬𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13088→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13086, 13087
13089→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 12925, 13088
13090→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗¬¬𝜎] into ax-1
13091→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13066, 13090
13092→→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2
13093→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13091, 13092
13094→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13089, 13093
13095→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜎] into ax-1
13096→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13097→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13095, 13096
13098→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
13099→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13097, 13098
13100→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2
13101→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑Modus ponens 13094, 13100
13102→→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13103→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑Modus ponens 13101, 13102
13104→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎𝜑] into ax-2
13105→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑Modus ponens 13103, 13104
13106→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑Modus ponens 13095, 13105
13107→→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑Subs [𝜑↗→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13108→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑Modus ponens 12954, 13107
13109→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎𝜑, 𝜒↗→¬¬𝜎¬¬𝜑] into ax-2
13110→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑Modus ponens 13108, 13109
13111→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑Modus ponens 13106, 13110
13112→→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎Subs [𝜑↗→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13113→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎Modus ponens 12960, 13112
13114→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎¬¬𝜑, 𝜒↗→¬𝜑¬𝜎] into ax-2
13115→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎Modus ponens 13113, 13114
13116→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎Modus ponens 13111, 13115
13117→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13118→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1
13119→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑Modus ponens 13117, 13118
13120→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑] into ax-2
13121→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑Modus ponens 13119, 13120
13122→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜑, 𝜒↗¬𝜎] into ax-2
13123→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13116, 13122
13124→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13125→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13123, 13124
13126→→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13127→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13125, 13126
13128→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13117, 13127
13129→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into id
13130→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13131→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13129, 13130
13132→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into notnotr
13133→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13134→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13135→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13133, 13134
13136→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13137→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13135, 13136
13138→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13132, 13137
13139→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13140→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13131, 13139
13141→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13142→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13140, 13141
13143→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13144→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13142, 13143
13145→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13146→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1
13147→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑Modus ponens 13145, 13146
13148→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑] into ax-2
13149→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑Modus ponens 13147, 13148
13150→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13151→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13138, 13150
13152→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13153→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13151, 13152
13154→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13155→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13153, 13154
13156→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13145, 13155
13157→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3
13158→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13159→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13157, 13158
13160→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13161→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13159, 13160
13162→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13156, 13161
13163→→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13164→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13162, 13163
13165→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13128, 13164
13166→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3
13167→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑Modus ponens 13165, 13166
13168→↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into biimp
13169→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13084, 13168
13170→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13171→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑Modus ponens 13167, 13170
13172→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗𝜑] into ax-2
13173→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13171, 13172
13174→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13169, 13173simp-7l
13175→→𝜓→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓Subs [𝜑↗→𝜓→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
13176→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓Modus ponens 12259, 13175
13177→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜓] into ax-2
13178→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓Modus ponens 13176, 13177
13179→𝜓→𝜎𝜓Subs [𝜑↗𝜓, 𝜓↗𝜎] into ax-1
13180→→𝜓→𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓Subs [𝜑↗→𝜓→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13181→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓Modus ponens 13179, 13180
13182→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜓] into ax-2
13183→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Modus ponens 13181, 13182
13184→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Modus ponens simp-5r, 13183
13185→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎, 𝜒↗𝜓] into ax-2
13186→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 13184, 13185
13187→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗¬¬𝜎] into ax-1
13188→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 13186, 13187
13189→→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2
13190→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 13188, 13189
13191→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12931, 13190
13192→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2
13193→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓Modus ponens 13191, 13192
13194→→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13195→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓Modus ponens 13193, 13194
13196→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎𝜓] into ax-2
13197→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓Modus ponens 13195, 13196
13198→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓Modus ponens 12939, 13197
13199→→𝜓¬¬𝜓→¬¬𝜎→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜎] into ax-1
13200→¬¬𝜎→𝜓¬¬𝜓Modus ponens 448, 13199
13201→→¬¬𝜎→𝜓¬¬𝜓→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓Subs [𝜑↗¬¬𝜎, 𝜒↗¬¬𝜓] into ax-2
13202→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓Modus ponens 13200, 13201
13203→→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓Subs [𝜑↗→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13204→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓Modus ponens 13202, 13203
13205→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎𝜓, 𝜒↗→¬¬𝜎¬¬𝜓] into ax-2
13206→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓Modus ponens 13204, 13205
13207→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓Modus ponens 13198, 13206
13208→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎Subs [𝜑↗¬𝜎, 𝜓↗¬𝜓] into ax-3
13209→→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎Subs [𝜑↗→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13210→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎Modus ponens 13208, 13209
13211→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎¬¬𝜓, 𝜒↗→¬𝜓¬𝜎] into ax-2
13212→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎Modus ponens 13210, 13211
13213→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎Modus ponens 13207, 13212
13214→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜓, 𝜒↗¬𝜎] into ax-2
13215→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13213, 13214
13216→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13217→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13215, 13216
13218→→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13219→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13217, 13218
13220→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12861, 13219
13221→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13222→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12973, 13221
13223→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13224→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13225→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13223, 13224
13226→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13227→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13225, 13226
13228→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 12976, 13227
13229→→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13230→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13222, 13229
13231→→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13232→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13230, 13231
13233→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13234→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13232, 13233
13235→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13236→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1
13237→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓Modus ponens 13235, 13236
13238→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓] into ax-2
13239→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓Modus ponens 13237, 13238
13240→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13241→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13228, 13240
13242→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13243→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13241, 13242
13244→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13245→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13243, 13244
13246→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13235, 13245
13247→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13248→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13001, 13247
13249→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13250→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13248, 13249
13251→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13246, 13250
13252→→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13253→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13251, 13252
13254→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎Modus ponens 13220, 13253
13255→→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3
13256→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓Modus ponens 13254, 13255
13257→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-1
13258→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓Modus ponens 13256, 13257
13259→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜓] into ax-2
13260→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓Modus ponens 13258, 13259
13261→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓Modus ponens 13013, 13260
13262→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13263→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓Modus ponens 13261, 13262
13264→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗𝜓] into ax-2
13265→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓Modus ponens 13263, 13264
13266→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓, 𝜓↗𝜎] into ax-1
13267→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓Modus ponens 13256, 13266
13268→→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓Subs [𝜑↗𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜓] into ax-2
13269→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓Modus ponens 13267, 13268
13270→→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓Subs [𝜑↗→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13271→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓Modus ponens 13269, 13270
13272→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→𝜎𝜓] into ax-2
13273→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Modus ponens 13271, 13272
13274→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗𝜎] into ax-1
13275→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 13186, 13274
13276→→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2
13277→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 13275, 13276
13278→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓Modus ponens 12926, 13277
13279→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2
13280→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Modus ponens 13278, 13279
13281→→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13282→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓Modus ponens 13280, 13281
13283→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜓] into ax-2
13284→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Modus ponens 13282, 13283
13285→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Modus ponens 13052, 13284
13286→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎, 𝜒↗𝜓] into ax-2
13287→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13285, 13286
13288→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗𝜎] into ax-1
13289→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13287, 13288
13290→→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2
13291→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13289, 13290
13292→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13060, 13291
13293→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2
13294→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Modus ponens 13292, 13293
13295→→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13296→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Modus ponens 13294, 13295
13297→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜓] into ax-2
13298→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Modus ponens 13296, 13297
13299→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗¬¬𝜎] into ax-1
13300→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13287, 13299
13301→→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2
13302→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13300, 13301
13303→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13089, 13302
13304→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2
13305→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓Modus ponens 13303, 13304
13306→→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13307→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓Modus ponens 13305, 13306
13308→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎𝜓] into ax-2
13309→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓Modus ponens 13307, 13308
13310→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓Modus ponens 13095, 13309
13311→→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓Subs [𝜑↗→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13312→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓Modus ponens 13202, 13311
13313→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎𝜓, 𝜒↗→¬¬𝜎¬¬𝜓] into ax-2
13314→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓Modus ponens 13312, 13313
13315→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓Modus ponens 13310, 13314
13316→→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎Subs [𝜑↗→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13317→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎Modus ponens 13208, 13316
13318→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎¬¬𝜓, 𝜒↗→¬𝜓¬𝜎] into ax-2
13319→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎Modus ponens 13317, 13318
13320→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎Modus ponens 13315, 13319
13321→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13322→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1
13323→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓Modus ponens 13321, 13322
13324→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓] into ax-2
13325→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓Modus ponens 13323, 13324
13326→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜓, 𝜒↗¬𝜎] into ax-2
13327→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13320, 13326
13328→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13329→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13327, 13328
13330→→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13331→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13329, 13330
13332→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13321, 13331
13333→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13334→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13129, 13333
13335→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13336→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13337→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13335, 13336
13338→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13339→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13337, 13338
13340→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13132, 13339
13341→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13342→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13334, 13341
13343→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13344→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13342, 13343
13345→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13346→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13344, 13345
13347→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13348→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1
13349→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓Modus ponens 13347, 13348
13350→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓] into ax-2
13351→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓Modus ponens 13349, 13350
13352→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13353→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13340, 13352
13354→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13355→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13353, 13354
13356→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13357→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13355, 13356
13358→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13347, 13357
13359→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13360→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13157, 13359
13361→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13362→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13360, 13361
13363→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13358, 13362
13364→→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13365→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13363, 13364
13366→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎Modus ponens 13332, 13365
13367→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3
13368→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓Modus ponens 13366, 13367
13369→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13370→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓Modus ponens 13368, 13369
13371→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗𝜓] into ax-2
13372→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13370, 13371
13373→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13169, 13372simp-7r
13374→→𝜑→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑Subs [𝜑↗→𝜑→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13375→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑Modus ponens 12458, 13374
13376→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜑, 𝜒↗→𝜁𝜑] into ax-2
13377→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑Modus ponens 13375, 13376
13378→𝜑→𝜌𝜑Subs [𝜓↗𝜌] into ax-1
13379→→𝜑→𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑Subs [𝜑↗→𝜑→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13380→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑Modus ponens 13378, 13379
13381→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜑, 𝜒↗→𝜌𝜑] into ax-2
13382→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Modus ponens 13380, 13381
13383→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Modus ponens simp-6l, 13382
13384↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into df-an
13385→¬¬𝜌𝜌Subs [𝜑↗𝜌] into notnotr
13386→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13387→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬¬𝜌] into ax-1
13388→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Modus ponens 13386, 13387
13389→→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Subs [𝜑↗¬¬𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-2
13390→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Modus ponens 13388, 13389
13391→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Modus ponens 13385, 13390
13392→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌, 𝜒↗𝜑] into ax-2
13393→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13383, 13392
13394→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗¬¬𝜌] into ax-1
13395→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13393, 13394
13396→→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2
13397→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13395, 13396
13398→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13391, 13397
13399→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜌] into ax-1
13400→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13401→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13399, 13400
13402→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
13403→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13401, 13402
13404→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2
13405→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑Modus ponens 13398, 13404
13406→→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13407→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑Modus ponens 13405, 13406
13408→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌𝜑] into ax-2
13409→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑Modus ponens 13407, 13408
13410→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑Modus ponens 13399, 13409
13411→→𝜑¬¬𝜑→¬¬𝜌→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜌] into ax-1
13412→¬¬𝜌→𝜑¬¬𝜑Modus ponens notnot, 13411
13413→→¬¬𝜌→𝜑¬¬𝜑→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑Subs [𝜑↗¬¬𝜌, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
13414→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑Modus ponens 13412, 13413
13415→→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑Subs [𝜑↗→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13416→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑Modus ponens 13414, 13415
13417→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌𝜑, 𝜒↗→¬¬𝜌¬¬𝜑] into ax-2
13418→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑Modus ponens 13416, 13417
13419→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑Modus ponens 13410, 13418
13420→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌Subs [𝜑↗¬𝜌, 𝜓↗¬𝜑] into ax-3
13421→→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌Subs [𝜑↗→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13422→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌Modus ponens 13420, 13421
13423→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌¬¬𝜑, 𝜒↗→¬𝜑¬𝜌] into ax-2
13424→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌Modus ponens 13422, 13423
13425→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌Modus ponens 13419, 13424
13426→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜑, 𝜒↗¬𝜌] into ax-2
13427→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13425, 13426
13428→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13429→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13427, 13428
13430→→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13431→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13429, 13430
13432→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13117, 13431
13433→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into id
13434→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13435→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13433, 13434
13436→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into notnotr
13437→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13438→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13439→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13437, 13438
13440→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13441→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13439, 13440
13442→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13436, 13441
13443→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13444→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13435, 13443
13445→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13446→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13444, 13445
13447→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13448→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13446, 13447
13449→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13450→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1
13451→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑Modus ponens 13449, 13450
13452→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑] into ax-2
13453→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑Modus ponens 13451, 13452
13454→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13455→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13442, 13454
13456→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13457→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13455, 13456
13458→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13459→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13457, 13458
13460→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13449, 13459
13461→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3
13462→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13463→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13461, 13462
13464→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13465→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13463, 13464
13466→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13460, 13465
13467→→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13468→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13466, 13467
13469→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13432, 13468
13470→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3
13471→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑Modus ponens 13469, 13470
13472→↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into biimp
13473→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13384, 13472
13474→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-1
13475→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑Modus ponens 13471, 13474
13476→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜑] into ax-2
13477→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑Modus ponens 13475, 13476
13478→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑Modus ponens 13473, 13477
13479→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into simpl
13480→↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into bicom1
13481↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Modus ponens 13384, 13480
13482→↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into biimp
13483→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Modus ponens 13481, 13482
13484→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13485→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑Modus ponens 13478, 13484
13486→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗𝜑] into ax-2
13487→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑Modus ponens 13485, 13486
13488→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into pm3.2im
13489→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑, 𝜓↗𝜌] into ax-1
13490→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑Modus ponens 13471, 13489
13491→→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑Subs [𝜑↗𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜑] into ax-2
13492→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑Modus ponens 13490, 13491
13493→→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑Subs [𝜑↗→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13494→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑Modus ponens 13492, 13493
13495→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→𝜌𝜑] into ax-2
13496→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Modus ponens 13494, 13495
13497→𝜌𝜌Subs [𝜑↗𝜌] into id
13498→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗𝜌] into ax-1
13499→𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Modus ponens 13386, 13498
13500→→𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Subs [𝜑↗𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-2
13501→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌Modus ponens 13499, 13500
13502→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗𝜌] into ax-1
13503→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13393, 13502
13504→→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2
13505→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13503, 13504
13506→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑Modus ponens 13386, 13505
13507→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into ax-1
13508→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13509→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13507, 13508
13510→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
13511→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13509, 13510
13512→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁Modus ponens 13479, 13511
13513→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2
13514→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Modus ponens 13506, 13513
13515→→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13516→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑Modus ponens 13514, 13515
13517→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜑] into ax-2
13518→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Modus ponens 13516, 13517
13519→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Modus ponens 13512, 13518
13520→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13521→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜌] into ax-1
13522→𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 13520, 13521
13523→→𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
13524→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 13522, 13523
13525→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌, 𝜒↗𝜑] into ax-2
13526→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13519, 13525
13527→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗𝜌] into ax-1
13528→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13526, 13527
13529→→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2
13530→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13528, 13529
13531→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13520, 13530
13532→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into id
13533→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into ax-1
13534→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13535→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13533, 13534
13536→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13537→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13535, 13536
13538→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2
13539→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Modus ponens 13531, 13538
13540→→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13541→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Modus ponens 13539, 13540
13542→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜑] into ax-2
13543→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Modus ponens 13541, 13542
13544↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into df-an
13545→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜌] into ax-1
13546→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 13520, 13545
13547→→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗¬¬𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
13548→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 13546, 13547
13549→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 13385, 13548
13550→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗¬¬𝜌] into ax-1
13551→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13526, 13550
13552→→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2
13553→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13551, 13552
13554→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13549, 13553
13555→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜌] into ax-1
13556→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13557→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13555, 13556
13558→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13559→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13557, 13558
13560→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2
13561→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑Modus ponens 13554, 13560
13562→→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13563→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑Modus ponens 13561, 13562
13564→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌𝜑] into ax-2
13565→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑Modus ponens 13563, 13564
13566→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑Modus ponens 13555, 13565
13567→→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑Subs [𝜑↗→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13568→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑Modus ponens 13414, 13567
13569→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌𝜑, 𝜒↗→¬¬𝜌¬¬𝜑] into ax-2
13570→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑Modus ponens 13568, 13569
13571→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑Modus ponens 13566, 13570
13572→→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌Subs [𝜑↗→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13573→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌Modus ponens 13420, 13572
13574→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌¬¬𝜑, 𝜒↗→¬𝜑¬𝜌] into ax-2
13575→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌Modus ponens 13573, 13574
13576→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌Modus ponens 13571, 13575
13577→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13578→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1
13579→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑Modus ponens 13577, 13578
13580→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑] into ax-2
13581→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑Modus ponens 13579, 13580
13582→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜑, 𝜒↗¬𝜌] into ax-2
13583→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13576, 13582
13584→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13585→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13583, 13584
13586→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13587→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13585, 13586
13588→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13577, 13587
13589→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into id
13590→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13591→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13589, 13590
13592→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into notnotr
13593→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13594→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13595→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13593, 13594
13596→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13597→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13595, 13596
13598→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13592, 13597
13599→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13600→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13591, 13599
13601→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13602→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13600, 13601
13603→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13604→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13602, 13603
13605→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13606→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1
13607→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑Modus ponens 13605, 13606
13608→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑] into ax-2
13609→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑Modus ponens 13607, 13608
13610→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13611→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13598, 13610
13612→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13613→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13611, 13612
13614→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13615→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13613, 13614
13616→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13605, 13615
13617→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3
13618→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13619→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13617, 13618
13620→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13621→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13619, 13620
13622→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13616, 13621
13623→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13624→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13622, 13623
13625→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13588, 13624
13626→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3
13627→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑Modus ponens 13625, 13626
13628→↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into biimp
13629→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13544, 13628
13630→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13631→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑Modus ponens 13627, 13630
13632→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗𝜑] into ax-2
13633→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 13631, 13632
13634→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 13629, 13633simp-8l
13635→→𝜓→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓Subs [𝜑↗→𝜓→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13636→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓Modus ponens 12719, 13635
13637→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜓] into ax-2
13638→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓Modus ponens 13636, 13637
13639→𝜓→𝜌𝜓Subs [𝜑↗𝜓, 𝜓↗𝜌] into ax-1
13640→→𝜓→𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓Subs [𝜑↗→𝜓→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13641→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓Modus ponens 13639, 13640
13642→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜓] into ax-2
13643→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Modus ponens 13641, 13642
13644→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Modus ponens simp-6r, 13643
13645→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌, 𝜒↗𝜓] into ax-2
13646→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13644, 13645
13647→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗¬¬𝜌] into ax-1
13648→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13646, 13647
13649→→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2
13650→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13648, 13649
13651→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13391, 13650
13652→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2
13653→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓Modus ponens 13651, 13652
13654→→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13655→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓Modus ponens 13653, 13654
13656→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌𝜓] into ax-2
13657→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓Modus ponens 13655, 13656
13658→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓Modus ponens 13399, 13657
13659→→𝜓¬¬𝜓→¬¬𝜌→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜌] into ax-1
13660→¬¬𝜌→𝜓¬¬𝜓Modus ponens 448, 13659
13661→→¬¬𝜌→𝜓¬¬𝜓→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓Subs [𝜑↗¬¬𝜌, 𝜒↗¬¬𝜓] into ax-2
13662→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓Modus ponens 13660, 13661
13663→→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓Subs [𝜑↗→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13664→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓Modus ponens 13662, 13663
13665→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌𝜓, 𝜒↗→¬¬𝜌¬¬𝜓] into ax-2
13666→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓Modus ponens 13664, 13665
13667→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓Modus ponens 13658, 13666
13668→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌Subs [𝜑↗¬𝜌, 𝜓↗¬𝜓] into ax-3
13669→→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌Subs [𝜑↗→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13670→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌Modus ponens 13668, 13669
13671→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌¬¬𝜓, 𝜒↗→¬𝜓¬𝜌] into ax-2
13672→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌Modus ponens 13670, 13671
13673→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌Modus ponens 13667, 13672
13674→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜓, 𝜒↗¬𝜌] into ax-2
13675→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13673, 13674
13676→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13677→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13675, 13676
13678→→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13679→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13677, 13678
13680→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13321, 13679
13681→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13682→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13433, 13681
13683→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13684→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13685→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13683, 13684
13686→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13687→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13685, 13686
13688→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13436, 13687
13689→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13690→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13682, 13689
13691→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13692→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13690, 13691
13693→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13694→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13692, 13693
13695→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13696→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1
13697→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓Modus ponens 13695, 13696
13698→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓] into ax-2
13699→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓Modus ponens 13697, 13698
13700→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13701→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13688, 13700
13702→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13703→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13701, 13702
13704→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13705→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13703, 13704
13706→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13695, 13705
13707→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13708→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13461, 13707
13709→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13710→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13708, 13709
13711→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13706, 13710
13712→→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13713→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13711, 13712
13714→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌Modus ponens 13680, 13713
13715→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3
13716→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓Modus ponens 13714, 13715
13717→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-1
13718→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓Modus ponens 13716, 13717
13719→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜓] into ax-2
13720→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓Modus ponens 13718, 13719
13721→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓Modus ponens 13473, 13720
13722→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13723→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓Modus ponens 13721, 13722
13724→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗𝜓] into ax-2
13725→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓Modus ponens 13723, 13724
13726→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓, 𝜓↗𝜌] into ax-1
13727→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓Modus ponens 13716, 13726
13728→→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓Subs [𝜑↗𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜓] into ax-2
13729→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓Modus ponens 13727, 13728
13730→→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓Subs [𝜑↗→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13731→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓Modus ponens 13729, 13730
13732→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→𝜌𝜓] into ax-2
13733→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Modus ponens 13731, 13732
13734→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗𝜌] into ax-1
13735→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13646, 13734
13736→→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2
13737→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13735, 13736
13738→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓Modus ponens 13386, 13737
13739→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2
13740→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Modus ponens 13738, 13739
13741→→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13742→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓Modus ponens 13740, 13741
13743→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜓] into ax-2
13744→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Modus ponens 13742, 13743
13745→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Modus ponens 13512, 13744
13746→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌, 𝜒↗𝜓] into ax-2
13747→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13745, 13746
13748→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗𝜌] into ax-1
13749→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13747, 13748
13750→→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2
13751→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13749, 13750
13752→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13520, 13751
13753→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2
13754→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Modus ponens 13752, 13753
13755→→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13756→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Modus ponens 13754, 13755
13757→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜓] into ax-2
13758→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Modus ponens 13756, 13757
13759→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗¬¬𝜌] into ax-1
13760→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13747, 13759
13761→→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2
13762→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13760, 13761
13763→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13549, 13762
13764→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2
13765→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓Modus ponens 13763, 13764
13766→→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13767→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓Modus ponens 13765, 13766
13768→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌𝜓] into ax-2
13769→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓Modus ponens 13767, 13768
13770→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓Modus ponens 13555, 13769
13771→→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓Subs [𝜑↗→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13772→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓Modus ponens 13662, 13771
13773→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌𝜓, 𝜒↗→¬¬𝜌¬¬𝜓] into ax-2
13774→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓Modus ponens 13772, 13773
13775→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓Modus ponens 13770, 13774
13776→→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌Subs [𝜑↗→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13777→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌Modus ponens 13668, 13776
13778→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌¬¬𝜓, 𝜒↗→¬𝜓¬𝜌] into ax-2
13779→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌Modus ponens 13777, 13778
13780→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌Modus ponens 13775, 13779
13781→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13782→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1
13783→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓Modus ponens 13781, 13782
13784→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓] into ax-2
13785→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓Modus ponens 13783, 13784
13786→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜓, 𝜒↗¬𝜌] into ax-2
13787→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13780, 13786
13788→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13789→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13787, 13788
13790→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13791→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13789, 13790
13792→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13781, 13791
13793→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13794→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13589, 13793
13795→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13796→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13797→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13795, 13796
13798→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13799→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13797, 13798
13800→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13592, 13799
13801→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13802→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13794, 13801
13803→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13804→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13802, 13803
13805→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13806→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13804, 13805
13807→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13808→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1
13809→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓Modus ponens 13807, 13808
13810→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓] into ax-2
13811→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓Modus ponens 13809, 13810
13812→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13813→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13800, 13812
13814→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13815→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13813, 13814
13816→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13817→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13815, 13816
13818→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13807, 13817
13819→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13820→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13617, 13819
13821→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13822→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13820, 13821
13823→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13818, 13822
13824→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13825→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13823, 13824
13826→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌Modus ponens 13792, 13825
13827→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3
13828→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓Modus ponens 13826, 13827
13829→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13830→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓Modus ponens 13828, 13829
13831→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗𝜓] into ax-2
13832→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 13830, 13831
13833→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 13629, 13832simp-8r
13834→→𝜑→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑Subs [𝜑↗→𝜑→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13835→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑Modus ponens 12918, 13834
13836→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜑, 𝜒↗→𝜎𝜑] into ax-2
13837→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑Modus ponens 13835, 13836
13838→𝜑→𝜇𝜑Subs [𝜓↗𝜇] into ax-1
13839→→𝜑→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑Subs [𝜑↗→𝜑→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13840→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑Modus ponens 13838, 13839
13841→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜑, 𝜒↗→𝜇𝜑] into ax-2
13842→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Modus ponens 13840, 13841
13843→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Modus ponens simp-7l, 13842
13844↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into df-an
13845→¬¬𝜇𝜇Subs [𝜑↗𝜇] into notnotr
13846→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13847→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬¬𝜇] into ax-1
13848→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Modus ponens 13846, 13847
13849→→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Subs [𝜑↗¬¬𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-2
13850→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Modus ponens 13848, 13849
13851→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Modus ponens 13845, 13850
13852→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇, 𝜒↗𝜑] into ax-2
13853→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13843, 13852
13854→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗¬¬𝜇] into ax-1
13855→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13853, 13854
13856→→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2
13857→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13855, 13856
13858→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13851, 13857
13859→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜇] into ax-1
13860→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13861→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13859, 13860
13862→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13863→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13861, 13862
13864→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2
13865→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑Modus ponens 13858, 13864
13866→→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13867→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑Modus ponens 13865, 13866
13868→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇𝜑] into ax-2
13869→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑Modus ponens 13867, 13868
13870→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑Modus ponens 13859, 13869
13871→→𝜑¬¬𝜑→¬¬𝜇→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜇] into ax-1
13872→¬¬𝜇→𝜑¬¬𝜑Modus ponens notnot, 13871
13873→→¬¬𝜇→𝜑¬¬𝜑→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑Subs [𝜑↗¬¬𝜇, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
13874→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑Modus ponens 13872, 13873
13875→→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑Subs [𝜑↗→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13876→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑Modus ponens 13874, 13875
13877→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇𝜑, 𝜒↗→¬¬𝜇¬¬𝜑] into ax-2
13878→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑Modus ponens 13876, 13877
13879→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑Modus ponens 13870, 13878
13880→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇Subs [𝜑↗¬𝜇, 𝜓↗¬𝜑] into ax-3
13881→→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇Subs [𝜑↗→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13882→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇Modus ponens 13880, 13881
13883→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇¬¬𝜑, 𝜒↗→¬𝜑¬𝜇] into ax-2
13884→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇Modus ponens 13882, 13883
13885→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇Modus ponens 13879, 13884
13886→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜑, 𝜒↗¬𝜇] into ax-2
13887→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13885, 13886
13888→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13889→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13887, 13888
13890→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13891→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13889, 13890
13892→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13577, 13891
13893→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into id
13894→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13895→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13893, 13894
13896→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into notnotr
13897→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13898→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
13899→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13897, 13898
13900→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13901→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13899, 13900
13902→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13896, 13901
13903→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13904→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13895, 13903
13905→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
13906→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13904, 13905
13907→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13908→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13906, 13907
13909→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
13910→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1
13911→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑Modus ponens 13909, 13910
13912→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑] into ax-2
13913→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑Modus ponens 13911, 13912
13914→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13915→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13902, 13914
13916→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13917→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13915, 13916
13918→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13919→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13917, 13918
13920→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13909, 13919
13921→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3
13922→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13923→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13921, 13922
13924→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13925→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13923, 13924
13926→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13920, 13925
13927→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13928→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13926, 13927
13929→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13892, 13928
13930→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3
13931→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑Modus ponens 13929, 13930
13932→↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into biimp
13933→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13844, 13932
13934→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-1
13935→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑Modus ponens 13931, 13934
13936→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜑] into ax-2
13937→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑Modus ponens 13935, 13936
13938→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑Modus ponens 13933, 13937
13939→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into simpl
13940→↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into bicom1
13941↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Modus ponens 13844, 13940
13942→↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into biimp
13943→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Modus ponens 13941, 13942
13944→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
13945→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑Modus ponens 13938, 13944
13946→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗𝜑] into ax-2
13947→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑Modus ponens 13945, 13946
13948→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into pm3.2im
13949→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑, 𝜓↗𝜇] into ax-1
13950→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑Modus ponens 13931, 13949
13951→→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑Subs [𝜑↗𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜑] into ax-2
13952→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑Modus ponens 13950, 13951
13953→→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑Subs [𝜑↗→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13954→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑Modus ponens 13952, 13953
13955→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→𝜇𝜑] into ax-2
13956→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Modus ponens 13954, 13955
13957→𝜇𝜇Subs [𝜑↗𝜇] into id
13958→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗𝜇] into ax-1
13959→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Modus ponens 13846, 13958
13960→→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Subs [𝜑↗𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-2
13961→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇Modus ponens 13959, 13960
13962→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗𝜇] into ax-1
13963→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13853, 13962
13964→→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2
13965→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13963, 13964
13966→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑Modus ponens 13846, 13965
13967→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into ax-1
13968→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13969→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13967, 13968
13970→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13971→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13969, 13970
13972→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎Modus ponens 13939, 13971
13973→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2
13974→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Modus ponens 13966, 13973
13975→→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13976→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑Modus ponens 13974, 13975
13977→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜑] into ax-2
13978→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Modus ponens 13976, 13977
13979→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Modus ponens 13972, 13978
13980→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13981→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜇] into ax-1
13982→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 13980, 13981
13983→→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
13984→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 13982, 13983
13985→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇, 𝜒↗𝜑] into ax-2
13986→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 13979, 13985
13987→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗𝜇] into ax-1
13988→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 13986, 13987
13989→→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2
13990→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 13988, 13989
13991→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 13980, 13990
13992→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into id
13993→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into ax-1
13994→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13995→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 13993, 13994
13996→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
13997→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 13995, 13996
13998→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2
13999→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Modus ponens 13991, 13998
14000→→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14001→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Modus ponens 13999, 14000
14002→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜑] into ax-2
14003→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Modus ponens 14001, 14002
14004↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into df-an
14005→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜇] into ax-1
14006→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 13980, 14005
14007→→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗¬¬𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14008→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14006, 14007
14009→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 13845, 14008
14010→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗¬¬𝜇] into ax-1
14011→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 13986, 14010
14012→→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2
14013→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14011, 14012
14014→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14009, 14013
14015→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜇] into ax-1
14016→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14017→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 14015, 14016
14018→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
14019→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 14017, 14018
14020→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2
14021→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑Modus ponens 14014, 14020
14022→→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14023→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑Modus ponens 14021, 14022
14024→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇𝜑] into ax-2
14025→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑Modus ponens 14023, 14024
14026→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑Modus ponens 14015, 14025
14027→→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑Subs [𝜑↗→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14028→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑Modus ponens 13874, 14027
14029→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇𝜑, 𝜒↗→¬¬𝜇¬¬𝜑] into ax-2
14030→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑Modus ponens 14028, 14029
14031→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑Modus ponens 14026, 14030
14032→→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇Subs [𝜑↗→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14033→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇Modus ponens 13880, 14032
14034→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇¬¬𝜑, 𝜒↗→¬𝜑¬𝜇] into ax-2
14035→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇Modus ponens 14033, 14034
14036→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇Modus ponens 14031, 14035
14037→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14038→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1
14039→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑Modus ponens 14037, 14038
14040→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑] into ax-2
14041→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑Modus ponens 14039, 14040
14042→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜑, 𝜒↗¬𝜇] into ax-2
14043→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14036, 14042
14044→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14045→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14043, 14044
14046→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14047→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14045, 14046
14048→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14037, 14047
14049→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into id
14050→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14051→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14049, 14050
14052→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into notnotr
14053→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14054→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14055→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14053, 14054
14056→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14057→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14055, 14056
14058→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14052, 14057
14059→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14060→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14051, 14059
14061→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14062→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14060, 14061
14063→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14064→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14062, 14063
14065→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14066→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1
14067→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑Modus ponens 14065, 14066
14068→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑] into ax-2
14069→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑Modus ponens 14067, 14068
14070→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14071→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14058, 14070
14072→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14073→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14071, 14072
14074→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14075→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14073, 14074
14076→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14065, 14075
14077→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3
14078→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14079→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14077, 14078
14080→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14081→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14079, 14080
14082→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14076, 14081
14083→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14084→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14082, 14083
14085→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14048, 14084
14086→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3
14087→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑Modus ponens 14085, 14086
14088→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into biimp
14089→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14004, 14088
14090→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14091→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑Modus ponens 14087, 14090
14092→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗𝜑] into ax-2
14093→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14091, 14092
14094→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14089, 14093simp-9l
14095→→𝜓→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓Subs [𝜑↗→𝜓→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
14096→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓Modus ponens 13179, 14095
14097→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜓] into ax-2
14098→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓Modus ponens 14096, 14097
14099→𝜓→𝜇𝜓Subs [𝜑↗𝜓, 𝜓↗𝜇] into ax-1
14100→→𝜓→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓Subs [𝜑↗→𝜓→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14101→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓Modus ponens 14099, 14100
14102→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜓] into ax-2
14103→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Modus ponens 14101, 14102
14104→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Modus ponens simp-7r, 14103
14105→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇, 𝜒↗𝜓] into ax-2
14106→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 14104, 14105
14107→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗¬¬𝜇] into ax-1
14108→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 14106, 14107
14109→→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2
14110→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 14108, 14109
14111→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13851, 14110
14112→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2
14113→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓Modus ponens 14111, 14112
14114→→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14115→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓Modus ponens 14113, 14114
14116→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇𝜓] into ax-2
14117→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓Modus ponens 14115, 14116
14118→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓Modus ponens 13859, 14117
14119→→𝜓¬¬𝜓→¬¬𝜇→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜇] into ax-1
14120→¬¬𝜇→𝜓¬¬𝜓Modus ponens 448, 14119
14121→→¬¬𝜇→𝜓¬¬𝜓→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓Subs [𝜑↗¬¬𝜇, 𝜒↗¬¬𝜓] into ax-2
14122→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓Modus ponens 14120, 14121
14123→→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓Subs [𝜑↗→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14124→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓Modus ponens 14122, 14123
14125→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇𝜓, 𝜒↗→¬¬𝜇¬¬𝜓] into ax-2
14126→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓Modus ponens 14124, 14125
14127→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓Modus ponens 14118, 14126
14128→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇Subs [𝜑↗¬𝜇, 𝜓↗¬𝜓] into ax-3
14129→→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇Subs [𝜑↗→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14130→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇Modus ponens 14128, 14129
14131→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇¬¬𝜓, 𝜒↗→¬𝜓¬𝜇] into ax-2
14132→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇Modus ponens 14130, 14131
14133→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇Modus ponens 14127, 14132
14134→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜓, 𝜒↗¬𝜇] into ax-2
14135→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14133, 14134
14136→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14137→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14135, 14136
14138→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14139→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14137, 14138
14140→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13781, 14139
14141→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14142→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13893, 14141
14143→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14144→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
14145→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14143, 14144
14146→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14147→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14145, 14146
14148→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13896, 14147
14149→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14150→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14142, 14149
14151→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
14152→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14150, 14151
14153→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14154→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14152, 14153
14155→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
14156→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1
14157→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓Modus ponens 14155, 14156
14158→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓] into ax-2
14159→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓Modus ponens 14157, 14158
14160→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14161→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14148, 14160
14162→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14163→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14161, 14162
14164→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14165→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14163, 14164
14166→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14155, 14165
14167→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14168→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 13921, 14167
14169→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14170→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14168, 14169
14171→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14166, 14170
14172→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14173→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14171, 14172
14174→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇Modus ponens 14140, 14173
14175→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3
14176→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓Modus ponens 14174, 14175
14177→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-1
14178→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓Modus ponens 14176, 14177
14179→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜓] into ax-2
14180→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓Modus ponens 14178, 14179
14181→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓Modus ponens 13933, 14180
14182→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
14183→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓Modus ponens 14181, 14182
14184→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗𝜓] into ax-2
14185→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓Modus ponens 14183, 14184
14186→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓, 𝜓↗𝜇] into ax-1
14187→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓Modus ponens 14176, 14186
14188→→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓Subs [𝜑↗𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜓] into ax-2
14189→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓Modus ponens 14187, 14188
14190→→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓Subs [𝜑↗→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14191→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓Modus ponens 14189, 14190
14192→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→𝜇𝜓] into ax-2
14193→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Modus ponens 14191, 14192
14194→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗𝜇] into ax-1
14195→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 14106, 14194
14196→→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2
14197→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 14195, 14196
14198→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓Modus ponens 13846, 14197
14199→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2
14200→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Modus ponens 14198, 14199
14201→→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14202→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓Modus ponens 14200, 14201
14203→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜓] into ax-2
14204→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Modus ponens 14202, 14203
14205→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Modus ponens 13972, 14204
14206→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇, 𝜒↗𝜓] into ax-2
14207→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14205, 14206
14208→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗𝜇] into ax-1
14209→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14207, 14208
14210→→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2
14211→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14209, 14210
14212→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 13980, 14211
14213→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2
14214→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Modus ponens 14212, 14213
14215→→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14216→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Modus ponens 14214, 14215
14217→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜓] into ax-2
14218→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Modus ponens 14216, 14217
14219→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗¬¬𝜇] into ax-1
14220→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14207, 14219
14221→→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2
14222→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14220, 14221
14223→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14009, 14222
14224→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2
14225→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓Modus ponens 14223, 14224
14226→→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14227→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓Modus ponens 14225, 14226
14228→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇𝜓] into ax-2
14229→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓Modus ponens 14227, 14228
14230→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓Modus ponens 14015, 14229
14231→→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓Subs [𝜑↗→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14232→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓Modus ponens 14122, 14231
14233→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇𝜓, 𝜒↗→¬¬𝜇¬¬𝜓] into ax-2
14234→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓Modus ponens 14232, 14233
14235→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓Modus ponens 14230, 14234
14236→→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇Subs [𝜑↗→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14237→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇Modus ponens 14128, 14236
14238→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇¬¬𝜓, 𝜒↗→¬𝜓¬𝜇] into ax-2
14239→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇Modus ponens 14237, 14238
14240→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇Modus ponens 14235, 14239
14241→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14242→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1
14243→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓Modus ponens 14241, 14242
14244→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓] into ax-2
14245→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓Modus ponens 14243, 14244
14246→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜓, 𝜒↗¬𝜇] into ax-2
14247→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14240, 14246
14248→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14249→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14247, 14248
14250→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14251→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14249, 14250
14252→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14241, 14251
14253→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14254→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14049, 14253
14255→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14256→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14257→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14255, 14256
14258→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14259→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14257, 14258
14260→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14052, 14259
14261→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14262→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14254, 14261
14263→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14264→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14262, 14263
14265→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14266→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14264, 14265
14267→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14268→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1
14269→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓Modus ponens 14267, 14268
14270→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓] into ax-2
14271→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓Modus ponens 14269, 14270
14272→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14273→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14260, 14272
14274→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14275→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14273, 14274
14276→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14277→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14275, 14276
14278→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14267, 14277
14279→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14280→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14077, 14279
14281→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14282→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14280, 14281
14283→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14278, 14282
14284→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14285→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14283, 14284
14286→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇Modus ponens 14252, 14285
14287→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3
14288→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓Modus ponens 14286, 14287
14289→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14290→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓Modus ponens 14288, 14289
14291→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗𝜓] into ax-2
14292→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14290, 14291
14293→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14089, 14292simp-9r
14294→→𝜑→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑Subs [𝜑↗→𝜑→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14295→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑Modus ponens 13378, 14294
14296→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜑, 𝜒↗→𝜌𝜑] into ax-2
14297→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑Modus ponens 14295, 14296
14298→𝜑→𝜆𝜑Subs [𝜓↗𝜆] into ax-1
14299→→𝜑→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑Subs [𝜑↗→𝜑→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14300→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑Modus ponens 14298, 14299
14301→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜑, 𝜒↗→𝜆𝜑] into ax-2
14302→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Modus ponens 14300, 14301
14303→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Modus ponens simp-8l, 14302
14304↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into df-an
14305→¬¬𝜆𝜆Subs [𝜑↗𝜆] into notnotr
14306→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14307→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬¬𝜆] into ax-1
14308→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Modus ponens 14306, 14307
14309→→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Subs [𝜑↗¬¬𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-2
14310→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Modus ponens 14308, 14309
14311→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Modus ponens 14305, 14310
14312→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆, 𝜒↗𝜑] into ax-2
14313→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14303, 14312
14314→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗¬¬𝜆] into ax-1
14315→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14313, 14314
14316→→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2
14317→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14315, 14316
14318→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14311, 14317
14319→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜆] into ax-1
14320→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14321→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 14319, 14320
14322→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
14323→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 14321, 14322
14324→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2
14325→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑Modus ponens 14318, 14324
14326→→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14327→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑Modus ponens 14325, 14326
14328→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆𝜑] into ax-2
14329→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑Modus ponens 14327, 14328
14330→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑Modus ponens 14319, 14329
14331→→𝜑¬¬𝜑→¬¬𝜆→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜆] into ax-1
14332→¬¬𝜆→𝜑¬¬𝜑Modus ponens notnot, 14331
14333→→¬¬𝜆→𝜑¬¬𝜑→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑Subs [𝜑↗¬¬𝜆, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
14334→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑Modus ponens 14332, 14333
14335→→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑Subs [𝜑↗→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14336→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑Modus ponens 14334, 14335
14337→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆𝜑, 𝜒↗→¬¬𝜆¬¬𝜑] into ax-2
14338→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑Modus ponens 14336, 14337
14339→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑Modus ponens 14330, 14338
14340→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆Subs [𝜑↗¬𝜆, 𝜓↗¬𝜑] into ax-3
14341→→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆Subs [𝜑↗→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14342→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆Modus ponens 14340, 14341
14343→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆¬¬𝜑, 𝜒↗→¬𝜑¬𝜆] into ax-2
14344→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆Modus ponens 14342, 14343
14345→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆Modus ponens 14339, 14344
14346→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜑, 𝜒↗¬𝜆] into ax-2
14347→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14345, 14346
14348→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14349→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14347, 14348
14350→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14351→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14349, 14350
14352→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14037, 14351
14353→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into id
14354→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14355→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14353, 14354
14356→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into notnotr
14357→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14358→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14359→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14357, 14358
14360→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14361→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14359, 14360
14362→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14356, 14361
14363→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14364→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14355, 14363
14365→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14366→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14364, 14365
14367→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14368→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14366, 14367
14369→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14370→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1
14371→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑Modus ponens 14369, 14370
14372→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑] into ax-2
14373→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑Modus ponens 14371, 14372
14374→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14375→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14362, 14374
14376→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14377→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14375, 14376
14378→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14379→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14377, 14378
14380→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14369, 14379
14381→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3
14382→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14383→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14381, 14382
14384→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14385→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14383, 14384
14386→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14380, 14385
14387→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14388→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14386, 14387
14389→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14352, 14388
14390→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3
14391→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑Modus ponens 14389, 14390
14392→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into biimp
14393→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14304, 14392
14394→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-1
14395→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑Modus ponens 14391, 14394
14396→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜑] into ax-2
14397→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑Modus ponens 14395, 14396
14398→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑Modus ponens 14393, 14397
14399→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into simpl
14400→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into bicom1
14401↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Modus ponens 14304, 14400
14402→↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into biimp
14403→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Modus ponens 14401, 14402
14404→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14405→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑Modus ponens 14398, 14404
14406→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗𝜑] into ax-2
14407→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑Modus ponens 14405, 14406
14408→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into pm3.2im
14409→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑, 𝜓↗𝜆] into ax-1
14410→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑Modus ponens 14391, 14409
14411→→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑Subs [𝜑↗𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜑] into ax-2
14412→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑Modus ponens 14410, 14411
14413→→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑Subs [𝜑↗→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14414→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑Modus ponens 14412, 14413
14415→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→𝜆𝜑] into ax-2
14416→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Modus ponens 14414, 14415
14417→𝜆𝜆Subs [𝜑↗𝜆] into id
14418→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗𝜆] into ax-1
14419→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Modus ponens 14306, 14418
14420→→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Subs [𝜑↗𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-2
14421→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆Modus ponens 14419, 14420
14422→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗𝜆] into ax-1
14423→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14313, 14422
14424→→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2
14425→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14423, 14424
14426→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑Modus ponens 14306, 14425
14427→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into ax-1
14428→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14429→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 14427, 14428
14430→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
14431→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 14429, 14430
14432→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌Modus ponens 14399, 14431
14433→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2
14434→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Modus ponens 14426, 14433
14435→→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14436→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑Modus ponens 14434, 14435
14437→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜑] into ax-2
14438→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Modus ponens 14436, 14437
14439→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Modus ponens 14432, 14438
14440→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14441→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜆] into ax-1
14442→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14440, 14441
14443→→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2
14444→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14442, 14443
14445→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆, 𝜒↗𝜑] into ax-2
14446→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14439, 14445
14447→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗𝜆] into ax-1
14448→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14446, 14447
14449→→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2
14450→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14448, 14449
14451→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14440, 14450
14452→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into id
14453→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into ax-1
14454→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14455→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14453, 14454
14456→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14457→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14455, 14456
14458→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2
14459→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Modus ponens 14451, 14458
14460→→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14461→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Modus ponens 14459, 14460
14462→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆𝜑] into ax-2
14463→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑Modus ponens 14461, 14462
14464↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into df-an
14465→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬¬𝜆] into ax-1
14466→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14440, 14465
14467→→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗¬¬𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2
14468→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14466, 14467
14469→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14305, 14468
14470→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗¬¬𝜆] into ax-1
14471→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14446, 14470
14472→→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2
14473→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14471, 14472
14474→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14469, 14473
14475→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜆] into ax-1
14476→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14477→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14475, 14476
14478→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14479→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14477, 14478
14480→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2
14481→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑Modus ponens 14474, 14480
14482→→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14483→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑Modus ponens 14481, 14482
14484→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆𝜑] into ax-2
14485→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑Modus ponens 14483, 14484
14486→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑Modus ponens 14475, 14485
14487→→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑Subs [𝜑↗→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14488→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑Modus ponens 14334, 14487
14489→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆𝜑, 𝜒↗→¬¬𝜆¬¬𝜑] into ax-2
14490→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑Modus ponens 14488, 14489
14491→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑Modus ponens 14486, 14490
14492→→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆Subs [𝜑↗→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14493→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆Modus ponens 14340, 14492
14494→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆¬¬𝜑, 𝜒↗→¬𝜑¬𝜆] into ax-2
14495→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆Modus ponens 14493, 14494
14496→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆Modus ponens 14491, 14495
14497→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14498→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1
14499→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑Modus ponens 14497, 14498
14500→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑] into ax-2
14501→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑Modus ponens 14499, 14500
14502→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜑, 𝜒↗¬𝜆] into ax-2
14503→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14496, 14502
14504→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14505→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14503, 14504
14506→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14507→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14505, 14506
14508→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14497, 14507
14509→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into id
14510→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14511→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14509, 14510
14512→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into notnotr
14513→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14514→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14515→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14513, 14514
14516→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14517→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14515, 14516
14518→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14512, 14517
14519→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14520→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14511, 14519
14521→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14522→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14520, 14521
14523→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14524→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14522, 14523
14525→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14526→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1
14527→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑Modus ponens 14525, 14526
14528→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑] into ax-2
14529→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑Modus ponens 14527, 14528
14530→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14531→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14518, 14530
14532→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14533→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14531, 14532
14534→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14535→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14533, 14534
14536→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14525, 14535
14537→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3
14538→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14539→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14537, 14538
14540→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14541→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14539, 14540
14542→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14536, 14541
14543→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14544→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14542, 14543
14545→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14508, 14544
14546→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3
14547→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑Modus ponens 14545, 14546
14548→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into biimp
14549→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14464, 14548
14550→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14551→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑Modus ponens 14547, 14550
14552→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗𝜑] into ax-2
14553→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14551, 14552
14554→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14549, 14553simp-10l
14555→→𝜓→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓Subs [𝜑↗→𝜓→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14556→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓Modus ponens 13639, 14555
14557→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜓] into ax-2
14558→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓Modus ponens 14556, 14557
14559→𝜓→𝜆𝜓Subs [𝜑↗𝜓, 𝜓↗𝜆] into ax-1
14560→→𝜓→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓Subs [𝜑↗→𝜓→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14561→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓Modus ponens 14559, 14560
14562→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜓] into ax-2
14563→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Modus ponens 14561, 14562
14564→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Modus ponens simp-8r, 14563
14565→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆, 𝜒↗𝜓] into ax-2
14566→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14564, 14565
14567→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗¬¬𝜆] into ax-1
14568→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14566, 14567
14569→→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2
14570→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14568, 14569
14571→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14311, 14570
14572→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2
14573→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓Modus ponens 14571, 14572
14574→→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14575→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓Modus ponens 14573, 14574
14576→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆𝜓] into ax-2
14577→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓Modus ponens 14575, 14576
14578→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓Modus ponens 14319, 14577
14579→→𝜓¬¬𝜓→¬¬𝜆→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜆] into ax-1
14580→¬¬𝜆→𝜓¬¬𝜓Modus ponens 448, 14579
14581→→¬¬𝜆→𝜓¬¬𝜓→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓Subs [𝜑↗¬¬𝜆, 𝜒↗¬¬𝜓] into ax-2
14582→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓Modus ponens 14580, 14581
14583→→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓Subs [𝜑↗→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14584→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓Modus ponens 14582, 14583
14585→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆𝜓, 𝜒↗→¬¬𝜆¬¬𝜓] into ax-2
14586→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓Modus ponens 14584, 14585
14587→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓Modus ponens 14578, 14586
14588→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆Subs [𝜑↗¬𝜆, 𝜓↗¬𝜓] into ax-3
14589→→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆Subs [𝜑↗→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14590→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆Modus ponens 14588, 14589
14591→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆¬¬𝜓, 𝜒↗→¬𝜓¬𝜆] into ax-2
14592→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆Modus ponens 14590, 14591
14593→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆Modus ponens 14587, 14592
14594→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜓, 𝜒↗¬𝜆] into ax-2
14595→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14593, 14594
14596→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14597→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14595, 14596
14598→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14599→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14597, 14598
14600→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14241, 14599
14601→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14602→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14353, 14601
14603→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14604→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14605→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14603, 14604
14606→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14607→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14605, 14606
14608→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14356, 14607
14609→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14610→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14602, 14609
14611→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14612→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14610, 14611
14613→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14614→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14612, 14613
14615→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14616→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1
14617→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓Modus ponens 14615, 14616
14618→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓] into ax-2
14619→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓Modus ponens 14617, 14618
14620→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14621→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14608, 14620
14622→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14623→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14621, 14622
14624→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14625→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14623, 14624
14626→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14615, 14625
14627→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14628→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14381, 14627
14629→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14630→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14628, 14629
14631→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14626, 14630
14632→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14633→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14631, 14632
14634→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆Modus ponens 14600, 14633
14635→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3
14636→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓Modus ponens 14634, 14635
14637→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-1
14638→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓Modus ponens 14636, 14637
14639→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜓] into ax-2
14640→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓Modus ponens 14638, 14639
14641→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓Modus ponens 14393, 14640
14642→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14643→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓Modus ponens 14641, 14642
14644→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗𝜓] into ax-2
14645→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓Modus ponens 14643, 14644
14646→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓, 𝜓↗𝜆] into ax-1
14647→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓Modus ponens 14636, 14646
14648→→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓Subs [𝜑↗𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜓] into ax-2
14649→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓Modus ponens 14647, 14648
14650→→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓Subs [𝜑↗→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14651→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓Modus ponens 14649, 14650
14652→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→𝜆𝜓] into ax-2
14653→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Modus ponens 14651, 14652
14654→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗𝜆] into ax-1
14655→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14566, 14654
14656→→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2
14657→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14655, 14656
14658→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓Modus ponens 14306, 14657
14659→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2
14660→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Modus ponens 14658, 14659
14661→→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14662→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓Modus ponens 14660, 14661
14663→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜓] into ax-2
14664→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Modus ponens 14662, 14663
14665→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Modus ponens 14432, 14664
14666→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆, 𝜒↗𝜓] into ax-2
14667→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14665, 14666
14668→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗𝜆] into ax-1
14669→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14667, 14668
14670→→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2
14671→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14669, 14670
14672→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14440, 14671
14673→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2
14674→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Modus ponens 14672, 14673
14675→→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14676→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Modus ponens 14674, 14675
14677→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆𝜓] into ax-2
14678→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓Modus ponens 14676, 14677
14679→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗¬¬𝜆] into ax-1
14680→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14667, 14679
14681→→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2
14682→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14680, 14681
14683→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14469, 14682
14684→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2
14685→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓Modus ponens 14683, 14684
14686→→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14687→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓Modus ponens 14685, 14686
14688→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆𝜓] into ax-2
14689→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓Modus ponens 14687, 14688
14690→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓Modus ponens 14475, 14689
14691→→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓Subs [𝜑↗→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14692→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓Modus ponens 14582, 14691
14693→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆𝜓, 𝜒↗→¬¬𝜆¬¬𝜓] into ax-2
14694→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓Modus ponens 14692, 14693
14695→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓Modus ponens 14690, 14694
14696→→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆Subs [𝜑↗→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14697→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆Modus ponens 14588, 14696
14698→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆¬¬𝜓, 𝜒↗→¬𝜓¬𝜆] into ax-2
14699→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆Modus ponens 14697, 14698
14700→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆Modus ponens 14695, 14699
14701→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14702→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1
14703→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓Modus ponens 14701, 14702
14704→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓] into ax-2
14705→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓Modus ponens 14703, 14704
14706→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜓, 𝜒↗¬𝜆] into ax-2
14707→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14700, 14706
14708→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14709→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14707, 14708
14710→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14711→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14709, 14710
14712→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14701, 14711
14713→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14714→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14509, 14713
14715→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14716→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14717→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14715, 14716
14718→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14719→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14717, 14718
14720→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14512, 14719
14721→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14722→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14714, 14721
14723→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14724→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14722, 14723
14725→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14726→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14724, 14725
14727→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14728→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1
14729→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓Modus ponens 14727, 14728
14730→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓] into ax-2
14731→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓Modus ponens 14729, 14730
14732→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14733→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14720, 14732
14734→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14735→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14733, 14734
14736→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14737→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14735, 14736
14738→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14727, 14737
14739→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14740→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14537, 14739
14741→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14742→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14740, 14741
14743→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14738, 14742
14744→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14745→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14743, 14744
14746→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆Modus ponens 14712, 14745
14747→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3
14748→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓Modus ponens 14746, 14747
14749→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14750→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓Modus ponens 14748, 14749
14751→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗𝜓] into ax-2
14752→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 14750, 14751
14753→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 14549, 14752simp-10r
14754→→𝜑→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑Subs [𝜑↗→𝜑→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14755→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑Modus ponens 13838, 14754
14756→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜑, 𝜒↗→𝜇𝜑] into ax-2
14757→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑Modus ponens 14755, 14756
14758→𝜑→𝜅𝜑Subs [𝜓↗𝜅] into ax-1
14759→→𝜑→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑Subs [𝜑↗→𝜑→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14760→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑Modus ponens 14758, 14759
14761→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜑, 𝜒↗→𝜅𝜑] into ax-2
14762→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Modus ponens 14760, 14761
14763→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Modus ponens simp-9l, 14762
14764↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into df-an
14765→¬¬𝜅𝜅Subs [𝜑↗𝜅] into notnotr
14766→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14767→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬¬𝜅] into ax-1
14768→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Modus ponens 14766, 14767
14769→→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Subs [𝜑↗¬¬𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-2
14770→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Modus ponens 14768, 14769
14771→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Modus ponens 14765, 14770
14772→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅, 𝜒↗𝜑] into ax-2
14773→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14763, 14772
14774→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗¬¬𝜅] into ax-1
14775→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14773, 14774
14776→→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2
14777→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14775, 14776
14778→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14771, 14777
14779→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜅] into ax-1
14780→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14781→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14779, 14780
14782→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14783→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14781, 14782
14784→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2
14785→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑Modus ponens 14778, 14784
14786→→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14787→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑Modus ponens 14785, 14786
14788→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅𝜑] into ax-2
14789→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑Modus ponens 14787, 14788
14790→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑Modus ponens 14779, 14789
14791→→𝜑¬¬𝜑→¬¬𝜅→𝜑¬¬𝜑Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜅] into ax-1
14792→¬¬𝜅→𝜑¬¬𝜑Modus ponens notnot, 14791
14793→→¬¬𝜅→𝜑¬¬𝜑→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑Subs [𝜑↗¬¬𝜅, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
14794→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑Modus ponens 14792, 14793
14795→→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑Subs [𝜑↗→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14796→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑Modus ponens 14794, 14795
14797→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅𝜑, 𝜒↗→¬¬𝜅¬¬𝜑] into ax-2
14798→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑Modus ponens 14796, 14797
14799→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑Modus ponens 14790, 14798
14800→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅Subs [𝜑↗¬𝜅, 𝜓↗¬𝜑] into ax-3
14801→→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅Subs [𝜑↗→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14802→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅Modus ponens 14800, 14801
14803→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅¬¬𝜑, 𝜒↗→¬𝜑¬𝜅] into ax-2
14804→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅Modus ponens 14802, 14803
14805→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅Modus ponens 14799, 14804
14806→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜑, 𝜒↗¬𝜅] into ax-2
14807→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14805, 14806
14808→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14809→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14807, 14808
14810→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14811→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14809, 14810
14812→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14497, 14811
14813→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into id
14814→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14815→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14813, 14814
14816→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into notnotr
14817→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14818→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
14819→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14817, 14818
14820→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14821→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14819, 14820
14822→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14816, 14821
14823→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14824→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14815, 14823
14825→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
14826→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14824, 14825
14827→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14828→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14826, 14827
14829→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
14830→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑, 𝜓↗¬𝜑] into ax-1
14831→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑Modus ponens 14829, 14830
14832→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑] into ax-2
14833→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑Modus ponens 14831, 14832
14834→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14835→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14822, 14834
14836→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14837→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14835, 14836
14838→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14839→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14837, 14838
14840→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14829, 14839
14841→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3
14842→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14843→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14841, 14842
14844→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14845→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14843, 14844
14846→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14840, 14845
14847→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14848→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14846, 14847
14849→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14812, 14848
14850→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3
14851→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑Modus ponens 14849, 14850
14852→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into biimp
14853→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14764, 14852
14854→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-1
14855→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑Modus ponens 14851, 14854
14856→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜑] into ax-2
14857→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑Modus ponens 14855, 14856
14858→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑Modus ponens 14853, 14857
14859→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into simpl
14860→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into bicom1
14861↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Modus ponens 14764, 14860
14862→↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into biimp
14863→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Modus ponens 14861, 14862
14864→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
14865→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑Modus ponens 14858, 14864
14866→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗𝜑] into ax-2
14867→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑Modus ponens 14865, 14866
14868→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into pm3.2im
14869→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑, 𝜓↗𝜅] into ax-1
14870→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑Modus ponens 14851, 14869
14871→→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑Subs [𝜑↗𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜑] into ax-2
14872→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑Modus ponens 14870, 14871
14873→→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑Subs [𝜑↗→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14874→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑Modus ponens 14872, 14873
14875→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→𝜅𝜑] into ax-2
14876→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Modus ponens 14874, 14875
14877→𝜅𝜅Subs [𝜑↗𝜅] into id
14878→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗𝜅] into ax-1
14879→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Modus ponens 14766, 14878
14880→→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Subs [𝜑↗𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-2
14881→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅Modus ponens 14879, 14880
14882→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗𝜅] into ax-1
14883→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14773, 14882
14884→→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2
14885→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14883, 14884
14886→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑Modus ponens 14766, 14885
14887→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into ax-1
14888→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14889→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14887, 14888
14890→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14891→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14889, 14890
14892→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇Modus ponens 14859, 14891
14893→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2
14894→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Modus ponens 14886, 14893
14895→→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14896→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑Modus ponens 14894, 14895
14897→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜑] into ax-2
14898→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Modus ponens 14896, 14897
14899→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Modus ponens 14892, 14898
14900→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14901→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗𝜅] into ax-1
14902→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Modus ponens 14900, 14901
14903→→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Subs [𝜑↗𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-2
14904→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Modus ponens 14902, 14903
14905→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅, 𝜒↗𝜑] into ax-2
14906→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14899, 14905
14907→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑, 𝜓↗𝜅] into ax-1
14908→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14906, 14907
14909→→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑] into ax-2
14910→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14908, 14909
14911→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14900, 14910
14912→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into id
14913→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅] into ax-1
14914→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14915→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14913, 14914
14916→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2
14917→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14915, 14916
14918→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜑] into ax-2
14919→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Modus ponens 14911, 14918
14920→→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14921→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Modus ponens 14919, 14920
14922→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅𝜑] into ax-2
14923→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑Modus ponens 14921, 14922
14924↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅] into df-an
14925→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬¬𝜅] into ax-1
14926→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Modus ponens 14900, 14925
14927→→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Subs [𝜑↗¬¬𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-2
14928→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Modus ponens 14926, 14927
14929→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅Modus ponens 14765, 14928
14930→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑, 𝜓↗¬¬𝜅] into ax-1
14931→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14906, 14930
14932→→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑] into ax-2
14933→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14931, 14932
14934→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑Modus ponens 14929, 14933
14935→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬¬𝜅] into ax-1
14936→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14937→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14935, 14936
14938→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2
14939→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆Modus ponens 14937, 14938
14940→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜑] into ax-2
14941→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑Modus ponens 14934, 14940
14942→→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14943→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑Modus ponens 14941, 14942
14944→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅𝜑] into ax-2
14945→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑Modus ponens 14943, 14944
14946→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑Modus ponens 14935, 14945
14947→→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑Subs [𝜑↗→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14948→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑Modus ponens 14794, 14947
14949→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅𝜑, 𝜒↗→¬¬𝜅¬¬𝜑] into ax-2
14950→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑Modus ponens 14948, 14949
14951→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑Modus ponens 14946, 14950
14952→→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅Subs [𝜑↗→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14953→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅Modus ponens 14800, 14952
14954→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅¬¬𝜑, 𝜒↗→¬𝜑¬𝜅] into ax-2
14955→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅Modus ponens 14953, 14954
14956→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅Modus ponens 14951, 14955
14957→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14958→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1
14959→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑Modus ponens 14957, 14958
14960→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑] into ax-2
14961→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑Modus ponens 14959, 14960
14962→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬𝜑, 𝜒↗¬𝜅] into ax-2
14963→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14956, 14962
14964→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14965→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14963, 14964
14966→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14967→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14965, 14966
14968→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14957, 14967
14969→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into id
14970→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14971→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14969, 14970
14972→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into notnotr
14973→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14974→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
14975→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14973, 14974
14976→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14977→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14975, 14976
14978→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14972, 14977
14979→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14980→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14971, 14979
14981→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
14982→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14980, 14981
14983→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14984→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14982, 14983
14985→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
14986→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑, 𝜓↗¬𝜑] into ax-1
14987→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑Modus ponens 14985, 14986
14988→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑] into ax-2
14989→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑Modus ponens 14987, 14988
14990→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14991→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14978, 14990
14992→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14993→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14991, 14992
14994→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14995→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14993, 14994
14996→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14985, 14995
14997→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3
14998→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14999→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14997, 14998
15000→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15001→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14999, 15000
15002→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14996, 15001
15003→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15004→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15002, 15003
15005→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14968, 15004
15006→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3
15007→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑Modus ponens 15005, 15006
15008→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into biimp
15009→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14924, 15008
15010→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-1
15011→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑Modus ponens 15007, 15010
15012→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗𝜑] into ax-2
15013→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑Modus ponens 15011, 15012
15014→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑Modus ponens 15009, 15013simp-11l
15015→→𝜓→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓Subs [𝜑↗→𝜓→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
15016→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓Modus ponens 14099, 15015
15017→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜓] into ax-2
15018→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓Modus ponens 15016, 15017
15019→𝜓→𝜅𝜓Subs [𝜑↗𝜓, 𝜓↗𝜅] into ax-1
15020→→𝜓→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓Subs [𝜑↗→𝜓→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15021→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓Modus ponens 15019, 15020
15022→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜓] into ax-2
15023→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Modus ponens 15021, 15022
15024→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Modus ponens simp-9r, 15023
15025→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅, 𝜒↗𝜓] into ax-2
15026→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 15024, 15025
15027→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗¬¬𝜅] into ax-1
15028→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 15026, 15027
15029→→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2
15030→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 15028, 15029
15031→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14771, 15030
15032→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2
15033→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓Modus ponens 15031, 15032
15034→→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15035→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓Modus ponens 15033, 15034
15036→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅𝜓] into ax-2
15037→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓Modus ponens 15035, 15036
15038→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓Modus ponens 14779, 15037
15039→→𝜓¬¬𝜓→¬¬𝜅→𝜓¬¬𝜓Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜅] into ax-1
15040→¬¬𝜅→𝜓¬¬𝜓Modus ponens 448, 15039
15041→→¬¬𝜅→𝜓¬¬𝜓→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓Subs [𝜑↗¬¬𝜅, 𝜒↗¬¬𝜓] into ax-2
15042→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓Modus ponens 15040, 15041
15043→→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓Subs [𝜑↗→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15044→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓Modus ponens 15042, 15043
15045→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅𝜓, 𝜒↗→¬¬𝜅¬¬𝜓] into ax-2
15046→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓Modus ponens 15044, 15045
15047→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓Modus ponens 15038, 15046
15048→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅Subs [𝜑↗¬𝜅, 𝜓↗¬𝜓] into ax-3
15049→→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅Subs [𝜑↗→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15050→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅Modus ponens 15048, 15049
15051→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅¬¬𝜓, 𝜒↗→¬𝜓¬𝜅] into ax-2
15052→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅Modus ponens 15050, 15051
15053→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅Modus ponens 15047, 15052
15054→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜓, 𝜒↗¬𝜅] into ax-2
15055→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15053, 15054
15056→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15057→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15055, 15056
15058→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15059→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15057, 15058
15060→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14701, 15059
15061→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15062→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14813, 15061
15063→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15064→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
15065→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15063, 15064
15066→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15067→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15065, 15066
15068→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14816, 15067
15069→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15070→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15062, 15069
15071→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
15072→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15070, 15071
15073→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15074→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15072, 15073
15075→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
15076→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓, 𝜓↗¬𝜓] into ax-1
15077→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓Modus ponens 15075, 15076
15078→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓] into ax-2
15079→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓Modus ponens 15077, 15078
15080→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15081→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15068, 15080
15082→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15083→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15081, 15082
15084→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15085→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15083, 15084
15086→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15075, 15085
15087→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15088→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 14841, 15087
15089→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15090→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15088, 15089
15091→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15086, 15090
15092→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15093→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15091, 15092
15094→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅Modus ponens 15060, 15093
15095→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3
15096→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓Modus ponens 15094, 15095
15097→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-1
15098→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓Modus ponens 15096, 15097
15099→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜓] into ax-2
15100→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓Modus ponens 15098, 15099
15101→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓Modus ponens 14853, 15100
15102→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
15103→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓Modus ponens 15101, 15102
15104→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗𝜓] into ax-2
15105→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓Modus ponens 15103, 15104
15106→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓, 𝜓↗𝜅] into ax-1
15107→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓Modus ponens 15096, 15106
15108→→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓Subs [𝜑↗𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜓] into ax-2
15109→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓Modus ponens 15107, 15108
15110→→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓Subs [𝜑↗→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15111→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓Modus ponens 15109, 15110
15112→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→𝜅𝜓] into ax-2
15113→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Modus ponens 15111, 15112
15114→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗𝜅] into ax-1
15115→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 15026, 15114
15116→→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2
15117→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 15115, 15116
15118→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓Modus ponens 14766, 15117
15119→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2
15120→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Modus ponens 15118, 15119
15121→→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15122→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓Modus ponens 15120, 15121
15123→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜓] into ax-2
15124→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Modus ponens 15122, 15123
15125→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Modus ponens 14892, 15124
15126→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅, 𝜒↗𝜓] into ax-2
15127→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 15125, 15126
15128→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓, 𝜓↗𝜅] into ax-1
15129→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 15127, 15128
15130→→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓] into ax-2
15131→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 15129, 15130
15132→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 14900, 15131
15133→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜓] into ax-2
15134→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Modus ponens 15132, 15133
15135→→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15136→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Modus ponens 15134, 15135
15137→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅𝜓] into ax-2
15138→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓Modus ponens 15136, 15137
15139→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓, 𝜓↗¬¬𝜅] into ax-1
15140→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 15127, 15139
15141→→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓] into ax-2
15142→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 15140, 15141
15143→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓Modus ponens 14929, 15142
15144→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜓] into ax-2
15145→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓Modus ponens 15143, 15144
15146→→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15147→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓Modus ponens 15145, 15146
15148→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅𝜓] into ax-2
15149→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓Modus ponens 15147, 15148
15150→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓Modus ponens 14935, 15149
15151→→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓Subs [𝜑↗→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15152→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓Modus ponens 15042, 15151
15153→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅𝜓, 𝜒↗→¬¬𝜅¬¬𝜓] into ax-2
15154→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓Modus ponens 15152, 15153
15155→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓Modus ponens 15150, 15154
15156→→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅Subs [𝜑↗→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15157→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅Modus ponens 15048, 15156
15158→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅¬¬𝜓, 𝜒↗→¬𝜓¬𝜅] into ax-2
15159→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅Modus ponens 15157, 15158
15160→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅Modus ponens 15155, 15159
15161→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15162→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1
15163→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓Modus ponens 15161, 15162
15164→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓] into ax-2
15165→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓Modus ponens 15163, 15164
15166→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬𝜓, 𝜒↗¬𝜅] into ax-2
15167→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15160, 15166
15168→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15169→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15167, 15168
15170→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15171→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15169, 15170
15172→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15161, 15171
15173→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15174→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14969, 15173
15175→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15176→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
15177→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15175, 15176
15178→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15179→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15177, 15178
15180→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14972, 15179
15181→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15182→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15174, 15181
15183→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
15184→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15182, 15183
15185→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15186→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15184, 15185
15187→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
15188→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓, 𝜓↗¬𝜓] into ax-1
15189→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓Modus ponens 15187, 15188
15190→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓] into ax-2
15191→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓Modus ponens 15189, 15190
15192→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15193→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15180, 15192
15194→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15195→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15193, 15194
15196→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15197→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15195, 15196
15198→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15187, 15197
15199→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15200→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 14997, 15199
15201→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15202→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15200, 15201
15203→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15198, 15202
15204→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15205→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15203, 15204
15206→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅Modus ponens 15172, 15205
15207→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3
15208→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓Modus ponens 15206, 15207
15209→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-1
15210→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓Modus ponens 15208, 15209
15211→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗𝜓] into ax-2
15212→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓Modus ponens 15210, 15211
15213→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓Modus ponens 15009, 15212simp-11r
15214↔⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓Subs [𝜓↗→𝜑𝜓] into df-an
15215→→𝜑→¬𝜓¬→𝜑𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓Subs [𝜓↗¬𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
15216→→𝜑¬𝜓→𝜑¬→𝜑𝜓Modus ponens jcn, 15215
15217→→→𝜑¬𝜓→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓Subs [𝜑↗→→𝜑¬𝜓→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15218→¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓Modus ponens 15216, 15217
15219→→¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬→𝜑𝜓Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬→𝜑𝜓] into ax-2
15220→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬→𝜑𝜓Modus ponens 15218, 15219
15221→¬𝜓→𝜑¬→𝜑𝜓Modus ponens 609, 15220
15222→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬→𝜑¬→𝜑𝜓] into id
15223→→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15224→¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15222, 15223
15225→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬→𝜑¬→𝜑𝜓] into notnotr
15226→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15227→→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1
15228→¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15226, 15227
15229→→¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗→¬𝜓¬→𝜑¬→𝜑𝜓] into ax-2
15230→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15228, 15229
15231→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15225, 15230
15232→→¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗¬→𝜑¬→𝜑𝜓] into ax-2
15233→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15224, 15232
15234→→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1
15235→¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15233, 15234
15236→→¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜒↗→¬𝜓¬→𝜑¬→𝜑𝜓] into ax-2
15237→→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15235, 15236
15238→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1
15239→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
15240→¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓Modus ponens 15238, 15239
15241→→¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬→𝜑𝜓¬𝜓] into ax-2
15242→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓Modus ponens 15240, 15241
15243→→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬→𝜑𝜓] into ax-2
15244→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15231, 15243
15245→→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15246→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15244, 15245
15247→→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬→𝜑𝜓¬𝜓, 𝜒↗→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓] into ax-2
15248→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15246, 15247
15249→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15238, 15248
15250→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬¬→𝜑¬→𝜑𝜓, 𝜓↗→𝜑¬→𝜑𝜓] into ax-3
15251→→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15252→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓Modus ponens 15250, 15251
15253→→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜒↗→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓] into ax-2
15254→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓Modus ponens 15252, 15253
15255→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓Modus ponens 15249, 15254
15256→→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→→¬𝜓→𝜑¬→𝜑𝜓→¬𝜓¬¬→𝜑¬→𝜑𝜓Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬→𝜑𝜓, 𝜒↗¬¬→𝜑¬→𝜑𝜓] into ax-2
15257→→¬𝜓→𝜑¬→𝜑𝜓→¬𝜓¬¬→𝜑¬→𝜑𝜓Modus ponens 15255, 15256
15258→¬𝜓¬¬→𝜑¬→𝜑𝜓Modus ponens 15221, 15257
15259→→¬𝜓¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓] into ax-3
15260→¬→𝜑¬→𝜑𝜓𝜓Modus ponens 15258, 15259
15261→↔⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓Subs [𝜑↗⋀𝜑→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓] into biimp
15262→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓Modus ponens 15214, 15261
15263→→¬→𝜑¬→𝜑𝜓𝜓→⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓Subs [𝜑↗→¬→𝜑¬→𝜑𝜓𝜓, 𝜓↗⋀𝜑→𝜑𝜓] into ax-1
15264→⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓Modus ponens 15260, 15263
15265→→⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓→→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓𝜓Subs [𝜑↗⋀𝜑→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗𝜓] into ax-2
15266→→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓𝜓Modus ponens 15264, 15265
15267→⋀𝜑→𝜑𝜓𝜓Modus ponens 15262, 15266pm3.35
15268→↔𝜓𝜒↔𝜓𝜒Subs [𝜑↗↔𝜓𝜒] into id
15269↔↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into bicom
15270→↔↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔↔𝜓𝜒↔𝜑𝜒] into biimp
15271→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒Modus ponens 15269, 15270
15272→→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15273→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒Modus ponens 15271, 15272
15274→→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜑𝜒↔𝜓𝜒, 𝜒↗↔↔𝜓𝜒↔𝜑𝜒] into ax-2
15275→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒Modus ponens 15273, 15274
15276→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒Modus ponens bibi1, 15275
15277→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜒] into biimp
15278→→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15279→↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒Modus ponens 15277, 15278
15280→→↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜓𝜒↔𝜑𝜒, 𝜒↗→↔𝜓𝜒↔𝜑𝜒] into ax-2
15281→→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Modus ponens 15279, 15280
15282→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Modus ponens 15276, 15281
15283→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15284→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗↔𝜓𝜒] into ax-1
15285→↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 15283, 15284
15286→→↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→→↔𝜓𝜒↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2
15287→→↔𝜓𝜒↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 15285, 15286
15288→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒, 𝜒↗↔𝜑𝜒] into ax-2
15289→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into ax-1
15290→↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 2744, 15289
15291→→↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15292→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 15290, 15291
15293→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 15283, 15292
15294→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒] into ax-1
15295→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15296→↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓Modus ponens 15294, 15295
15297→→↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜓𝜒↔𝜑𝜓] into ax-2
15298→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓Modus ponens 15296, 15297
15299→→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15300→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Modus ponens 15293, 15299
15301→→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15302→↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Modus ponens 15300, 15301
15303→→↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜓𝜒↔𝜑𝜓, 𝜒↗→↔𝜓𝜒↔𝜑𝜒] into ax-2
15304→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒Modus ponens 15302, 15303
15305↔⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒] into df-an
15306→¬¬↔𝜓𝜒↔𝜓𝜒Subs [𝜑↗↔𝜓𝜒] into notnotr
15307→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1
15308→¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 15283, 15307
15309→→¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→→¬¬↔𝜓𝜒↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2
15310→→¬¬↔𝜓𝜒↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 15308, 15309
15311→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒Modus ponens 15306, 15310
15312→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1
15313→¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 2744, 15312
15314→→¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15315→→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 15313, 15314
15316→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 15311, 15315
15317→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬↔𝜓𝜒] into ax-1
15318→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15319→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓Modus ponens 15317, 15318
15320→→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬↔𝜓𝜒↔𝜑𝜓] into ax-2
15321→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓Modus ponens 15319, 15320
15322→→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15323→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒Modus ponens 15316, 15322
15324→→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15325→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒Modus ponens 15323, 15324
15326→→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒↔𝜑𝜓, 𝜒↗→¬¬↔𝜓𝜒↔𝜑𝜒] into ax-2
15327→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒Modus ponens 15325, 15326
15328→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒Modus ponens 15317, 15327
15329→↔𝜑𝜒¬¬↔𝜑𝜒Subs [𝜑↗↔𝜑𝜒] into notnot
15330→→↔𝜑𝜒¬¬↔𝜑𝜒→¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜒¬¬↔𝜑𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1
15331→¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒Modus ponens 15329, 15330
15332→→¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜑𝜒, 𝜒↗¬¬↔𝜑𝜒] into ax-2
15333→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒Modus ponens 15331, 15332
15334→→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒Subs [𝜑↗→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15335→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒Modus ponens 15333, 15334
15336→→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒↔𝜑𝜒, 𝜒↗→¬¬↔𝜓𝜒¬¬↔𝜑𝜒] into ax-2
15337→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒Modus ponens 15335, 15336
15338→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒Modus ponens 15328, 15337
15339→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒Subs [𝜑↗¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-3
15340→→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒Subs [𝜑↗→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15341→↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒Modus ponens 15339, 15340
15342→→↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒¬¬↔𝜑𝜒, 𝜒↗→¬↔𝜑𝜒¬↔𝜓𝜒] into ax-2
15343→→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒Modus ponens 15341, 15342
15344→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒Modus ponens 15338, 15343
15345→¬↔𝜑𝜒¬↔𝜑𝜒Subs [𝜑↗¬↔𝜑𝜒] into id
15346→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15347→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒Subs [𝜑↗→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15348→¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒Modus ponens 15346, 15347
15349→→¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜑𝜒] into ax-2
15350→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒Modus ponens 15348, 15349
15351→→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬↔𝜓𝜒] into ax-2
15352→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15344, 15351
15353→→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15354→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15352, 15353
15355→→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15356→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15354, 15355
15357→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15346, 15356
15358→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒] into id
15359→→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15360→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15358, 15359
15361→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒] into notnotr
15362→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15363→→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1
15364→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15362, 15363
15365→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15366→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15364, 15365
15367→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15361, 15366
15368→→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15369→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15360, 15368
15370→→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1
15371→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15369, 15370
15372→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15373→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15371, 15372
15374→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1
15375→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒Subs [𝜑↗→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15376→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒Modus ponens 15374, 15375
15377→→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒] into ax-2
15378→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒Modus ponens 15376, 15377
15379→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15380→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15367, 15379
15381→→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15382→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15380, 15381
15383→→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15384→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15382, 15383
15385→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15374, 15384
15386→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜓𝜒] into ax-3
15387→→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15388→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15386, 15387
15389→→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15390→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15388, 15389
15391→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15385, 15390
15392→→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15393→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15391, 15392
15394→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15357, 15393
15395→→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-3
15396→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒Modus ponens 15394, 15395
15397→↔⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Subs [𝜑↗⋀↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒] into biimp
15398→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒Modus ponens 15305, 15397
15399→→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒→⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜓↔𝜓𝜒] into ax-1
15400→⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒Modus ponens 15396, 15399
15401→→⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒→→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒Subs [𝜑↗⋀↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗↔𝜑𝜒] into ax-2
15402→→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒Modus ponens 15400, 15401
15403→⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒Modus ponens 15398, 15402bitr
15404→↔𝜒𝜓↔𝜒𝜓Subs [𝜑↗↔𝜒𝜓] into id
15405↔→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into pm5.74
15406→↔→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗→↔𝜒𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp
15407→→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15405, 15406
15408↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15404, 15407
15409→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into id
15410→↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-1
15411→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15408, 15410
15412↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74
15413→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp
15414→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Modus ponens 15412, 15413
15415↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Modus ponens 15409, 15414
15416↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74
15417→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp
15418→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15416, 15417
15419↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15411, 15418
15420→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp
15421→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15419, 15420
15422→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp
15423→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Modus ponens 15415, 15422
15424→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into ax-1
15425→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15421, 15424
15426→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into ax-2
15427→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15425, 15426
15428→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15423, 15427
15429→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into bicom1
15430↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Modus ponens 15419, 15429
15431→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp
15432→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒Modus ponens 15430, 15431
15433→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into bicom1
15434↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Modus ponens 15415, 15433
15435→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into biimp
15436→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Modus ponens 15434, 15435
15437→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into ax-1
15438→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Modus ponens 15436, 15437
15439→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into ax-2
15440→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Modus ponens 15438, 15439
15441→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑Modus ponens 15432, 15440
15442→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into impbi
15443→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15428, 15442
15444↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Modus ponens 15441, 15443
15445↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74
15446→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into bicom1
15447↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Modus ponens 15445, 15446
15448→↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp
15449→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Modus ponens 15447, 15448
15450→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Modus ponens 15444, 15449
15451→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into id
15452→↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜓] into bicom1
15453↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15408, 15452
15454→↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into ax-1
15455→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15453, 15454
15456↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74
15457→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp
15458→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Modus ponens 15456, 15457
15459↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Modus ponens 15451, 15458
15460↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜓, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74
15461→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into biimp
15462→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15460, 15461
15463↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15455, 15462
15464→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into biimp
15465→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15463, 15464
15466→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp
15467→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Modus ponens 15459, 15466
15468→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into ax-1
15469→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15465, 15468
15470→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into ax-2
15471→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15469, 15470
15472→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15467, 15471
15473→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into bicom1
15474↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Modus ponens 15463, 15473
15475→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp
15476→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓Modus ponens 15474, 15475
15477→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into bicom1
15478↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Modus ponens 15459, 15477
15479→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into biimp
15480→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Modus ponens 15478, 15479
15481→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into ax-1
15482→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Modus ponens 15480, 15481
15483→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into ax-2
15484→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Modus ponens 15482, 15483
15485→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑Modus ponens 15476, 15484
15486→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into impbi
15487→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15472, 15486
15488↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Modus ponens 15485, 15487
15489↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74
15490→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into bicom1
15491↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15489, 15490
15492→↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp
15493→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15491, 15492
15494→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15488, 15493
15495→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into impbi
15496→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Modus ponens 15450, 15495
15497↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Modus ponens 15494, 15496
15498↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜑] into pm5.74
15499↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74
15500→↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into bicom1
15501↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓Modus ponens 15499, 15500
15502→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into biimp
15503→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓Modus ponens 15501, 15502
15504→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp
15505→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-1
15506→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓Modus ponens 15503, 15505
15507→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2
15508→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15506, 15507
15509→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15450, 15508
15510→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into bicom1
15511→↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp
15512→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓Modus ponens 15499, 15511
15513→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into bicom1
15514↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15497, 15513
15515→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp
15516→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into ax-1
15517→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15494, 15516
15518→→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜒↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-2
15519→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15517, 15518
15520→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15512, 15519
15521→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into impbi
15522→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15509, 15521
15523↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15520, 15522
15524→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into biimp
15525→↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp
15526→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15498, 15525
15527→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜒] into ax-1
15528→→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15509, 15527
15529→→→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2
15530→→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15528, 15529
15531→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15526, 15530
15532→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into bicom1
15533↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Modus ponens 15523, 15532
15534→↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp
15535→↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into bicom1
15536↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒Modus ponens 15498, 15535
15537→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜒] into biimp
15538→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒Modus ponens 15536, 15537
15539→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into ax-1
15540→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒Modus ponens 15538, 15539
15541→→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓↔𝜑𝜒] into ax-2
15542→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Modus ponens 15540, 15541
15543→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Modus ponens 15520, 15542
15544→→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into impbi
15545→→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15531, 15544
15546↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓Modus ponens 15543, 15545
15547↔→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
15548→↔→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓Subs [𝜑↗→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓] into bicom1
15549↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓Modus ponens 15547, 15548
15550→↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓Subs [𝜑↗↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓] into biimp
15551→↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓Modus ponens 15549, 15550
15552→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓Modus ponens 15546, 15551
15553↔↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into bicom
15554→↔↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓↔𝜑𝜒] into biimp
15555→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒Modus ponens 15553, 15554
15556→→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1
15557→↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒Modus ponens 15555, 15556
15558→→↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔↔𝜑𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓↔𝜑𝜒] into ax-2
15559→→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒Modus ponens 15557, 15558
15560→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒Modus ponens 15552, 15559
15561→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒] into biimp
15562→→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1
15563→↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒Modus ponens 15561, 15562
15564→→↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔↔𝜑𝜓↔𝜑𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15565→→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 15563, 15564
15566→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 15560, 15565
15567→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓] into ax-1
15568→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15569→↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓Modus ponens 15567, 15568
15570→→↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2
15571→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓Modus ponens 15569, 15570
15572→→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15573→→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15574→↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Modus ponens 15543, 15573
15575→→↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜒] into ax-2
15576→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Modus ponens 15574, 15575
15577→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒Modus ponens 15567, 15576
15578→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15579→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔𝜒𝜓] into ax-1
15580→↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Modus ponens 15578, 15579
15581→→↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→→↔𝜒𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
15582→→↔𝜒𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Modus ponens 15580, 15581
15583→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15584→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1
15585→↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 2705, 15584
15586→→↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15587→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 15585, 15586
15588↔⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓] into df-an
15589→¬¬↔𝜒𝜓↔𝜒𝜓Subs [𝜑↗↔𝜒𝜓] into notnotr
15590→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬¬↔𝜒𝜓] into ax-1
15591→¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Modus ponens 15578, 15590
15592→→¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→→¬¬↔𝜒𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
15593→→¬¬↔𝜒𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Modus ponens 15591, 15592
15594→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓Modus ponens 15589, 15593
15595→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗¬¬↔𝜒𝜓] into ax-1
15596→¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 2705, 15595
15597→→¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15598→→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 15596, 15597
15599→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒Modus ponens 15594, 15598
15600→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬↔𝜒𝜓] into ax-1
15601→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15602→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓Modus ponens 15600, 15601
15603→→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬↔𝜒𝜓↔𝜑𝜓] into ax-2
15604→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓Modus ponens 15602, 15603
15605→→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15606→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒Modus ponens 15599, 15605
15607→→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15608→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒Modus ponens 15606, 15607
15609→→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓↔𝜑𝜓, 𝜒↗→¬¬↔𝜒𝜓↔𝜑𝜒] into ax-2
15610→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒Modus ponens 15608, 15609
15611→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒Modus ponens 15600, 15610
15612→→↔𝜑𝜒¬¬↔𝜑𝜒→¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒Subs [𝜑↗→↔𝜑𝜒¬¬↔𝜑𝜒, 𝜓↗¬¬↔𝜒𝜓] into ax-1
15613→¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒Modus ponens 15329, 15612
15614→→¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗¬¬↔𝜑𝜒] into ax-2
15615→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒Modus ponens 15613, 15614
15616→→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒Subs [𝜑↗→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15617→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒Modus ponens 15615, 15616
15618→→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓↔𝜑𝜒, 𝜒↗→¬¬↔𝜒𝜓¬¬↔𝜑𝜒] into ax-2
15619→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒Modus ponens 15617, 15618
15620→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒Modus ponens 15611, 15619
15621→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓Subs [𝜑↗¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-3
15622→→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓→↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓Subs [𝜑↗→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15623→↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓Modus ponens 15621, 15622
15624→→↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓→→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓¬¬↔𝜑𝜒, 𝜒↗→¬↔𝜑𝜒¬↔𝜒𝜓] into ax-2
15625→→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓Modus ponens 15623, 15624
15626→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓Modus ponens 15620, 15625
15627→→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬↔𝜒𝜓] into ax-2
15628→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15626, 15627
15629→→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15630→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15628, 15629
15631→→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15632→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15630, 15631
15633→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15346, 15632
15634→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓] into id
15635→→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15636→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15634, 15635
15637→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓] into notnotr
15638→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15639→→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1
15640→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15638, 15639
15641→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15642→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15640, 15641
15643→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15637, 15642
15644→→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15645→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15636, 15644
15646→→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1
15647→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15645, 15646
15648→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15649→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15647, 15648
15650→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1
15651→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒Subs [𝜑↗→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15652→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒Modus ponens 15650, 15651
15653→→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒] into ax-2
15654→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒Modus ponens 15652, 15653
15655→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15656→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15643, 15655
15657→→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15658→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15656, 15657
15659→→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15660→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15658, 15659
15661→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15650, 15660
15662→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗→↔𝜑𝜓¬↔𝜒𝜓] into ax-3
15663→→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15664→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15662, 15663
15665→→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15666→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15664, 15665
15667→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15661, 15666
15668→→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15669→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15667, 15668
15670→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15633, 15669
15671→→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-3
15672→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒Modus ponens 15670, 15671
15673→↔⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Subs [𝜑↗⋀↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓] into biimp
15674→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓Modus ponens 15588, 15673
15675→→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒→⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜓↔𝜒𝜓] into ax-1
15676→⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒Modus ponens 15672, 15675
15677→→⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒→→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒Subs [𝜑↗⋀↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15678→→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒Modus ponens 15676, 15677
15679→⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒Modus ponens 15674, 15678biantr
15680↔→𝜓𝜒→¬𝜒¬𝜓Subs [𝜑↗𝜓, 𝜓↗𝜒] into con34b
15681→↔→𝜓𝜒→¬𝜒¬𝜓→𝜑↔→𝜓𝜒→¬𝜒¬𝜓Subs [𝜑↗↔→𝜓𝜒→¬𝜒¬𝜓, 𝜓↗𝜑] into ax-1
15682→𝜑↔→𝜓𝜒→¬𝜒¬𝜓Modus ponens 15680, 15681
15683↔→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓Subs [𝜓↗→𝜓𝜒, 𝜒↗→¬𝜒¬𝜓] into pm5.74
15684→↔→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓Subs [𝜑↗→𝜑↔→𝜓𝜒→¬𝜒¬𝜓, 𝜓↗↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓] into biimp
15685→→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓Modus ponens 15683, 15684
15686↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓Modus ponens 15682, 15685
15687↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓Subs [𝜓↗¬𝜒, 𝜒↗¬𝜓] into impexp
15688→↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓] into bicom1
15689↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓Modus ponens 15687, 15688
15690→↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp
15691→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓Modus ponens 15689, 15690
15692→↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓] into biimp
15693→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓Modus ponens 15686, 15692
15694→→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1
15695→→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓Modus ponens 15691, 15694
15696→→→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓, 𝜒↗→⋀𝜑¬𝜒¬𝜓] into ax-2
15697→→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens 15695, 15696
15698→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens 15693, 15697
15699→↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into bicom1
15700→↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓] into biimp
15701→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓Modus ponens 15687, 15700
15702→↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓] into bicom1
15703↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒Modus ponens 15686, 15702
15704→↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into biimp
15705→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒Modus ponens 15703, 15704
15706→→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into ax-1
15707→→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒Modus ponens 15705, 15706
15708→→→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓, 𝜒↗→𝜑→𝜓𝜒] into ax-2
15709→→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒Modus ponens 15707, 15708
15710→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒Modus ponens 15701, 15709
15711→→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into impbi
15712→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens 15698, 15711
15713↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens 15710, 15712
15714→↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp
15715→↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into biimp
15716→→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
15717→→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens 15698, 15716
15718→→→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑¬𝜒¬𝜓] into ax-2
15719→→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens 15717, 15718
15720→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens pm3.3, 15719pm3.37
15721→↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into bicom1
15722↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒Modus ponens 15713, 15721
15723→↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into biimp
15724→↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into bicom1
15725↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens impexp, 15724
15726→↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into biimp
15727→→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into ax-1
15728→→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens pm3.31, 15727
15729→→→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
15730→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒Modus ponens 15728, 15729
15731→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒Modus ponens 15710, 15730
15732→→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into impbi
15733→→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens pm3.37, 15732
15734↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓Modus ponens 15731, 15733pm4.14
15735→↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp
15736→→𝜒𝜃→𝜒𝜃Subs [𝜑↗→𝜒𝜃] into id
15737→→𝜑→→𝜑𝜓𝜑→⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗⋀𝜑𝜒] into ax-1
15738→⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑Modus ponens 25, 15737
15739→→⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑→→⋀𝜑𝜒𝜑→⋀𝜑𝜒→→𝜑𝜓𝜑Subs [𝜑↗⋀𝜑𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2
15740→→⋀𝜑𝜒𝜑→⋀𝜑𝜒→→𝜑𝜓𝜑Modus ponens 15738, 15739
15741→⋀𝜑𝜒→→𝜑𝜓𝜑Modus ponens 8604, 15740
15742→→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗⋀𝜑𝜒] into ax-1
15743→⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓Modus ponens 31, 15742
15744→→⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→⋀𝜑𝜒→→𝜑𝜓𝜑→⋀𝜑𝜒→→𝜑𝜓𝜓Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2
15745→→⋀𝜑𝜒→→𝜑𝜓𝜑→⋀𝜑𝜒→→𝜑𝜓𝜓Modus ponens 15743, 15744
15746→⋀𝜑𝜒→→𝜑𝜓𝜓Modus ponens 15741, 15745
15747→→⋀𝜑𝜒→→𝜑𝜓𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2
15748→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓Modus ponens 15746, 15747
15749→→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓Subs [𝜑↗→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
15750→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓Modus ponens 15748, 15749
15751→→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜓] into ax-2
15752→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜓Modus ponens 15750, 15751
15753→→𝜑𝜓→⋀𝜑𝜒𝜓Modus ponens 7486, 15752
15754→⋀𝜑𝜒𝜒Subs [𝜓↗𝜒] into simpr
15755→𝜒→→𝜒𝜃𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜒𝜃] into ax-1
15756→→𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒Subs [𝜑↗→𝜒→→𝜒𝜃𝜒, 𝜓↗⋀𝜑𝜒] into ax-1
15757→⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒Modus ponens 15755, 15756
15758→→⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒→→⋀𝜑𝜒𝜒→⋀𝜑𝜒→→𝜒𝜃𝜒Subs [𝜑↗⋀𝜑𝜒, 𝜓↗𝜒, 𝜒↗→→𝜒𝜃𝜒] into ax-2
15759→→⋀𝜑𝜒𝜒→⋀𝜑𝜒→→𝜒𝜃𝜒Modus ponens 15757, 15758
15760→⋀𝜑𝜒→→𝜒𝜃𝜒Modus ponens 15754, 15759
15761→→→𝜒𝜃→𝜒𝜃→→→𝜒𝜃𝜒→→𝜒𝜃𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗𝜒, 𝜒↗𝜃] into ax-2
15762→→→𝜒𝜃𝜒→→𝜒𝜃𝜃Modus ponens 15736, 15761
15763→→→→𝜒𝜃𝜒→→𝜒𝜃𝜃→⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃Subs [𝜑↗→→→𝜒𝜃𝜒→→𝜒𝜃𝜃, 𝜓↗⋀𝜑𝜒] into ax-1
15764→⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃Modus ponens 15762, 15763
15765→→⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃→→⋀𝜑𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→→𝜒𝜃𝜃Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→→𝜒𝜃𝜒, 𝜒↗→→𝜒𝜃𝜃] into ax-2
15766→→⋀𝜑𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→→𝜒𝜃𝜃Modus ponens 15764, 15765
15767→⋀𝜑𝜒→→𝜒𝜃𝜃Modus ponens 15760, 15766
15768→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗⋀𝜑𝜒] into ax-1
15769→→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃Subs [𝜑↗→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15770→→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃Modus ponens 15768, 15769
15771→→→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒→𝜒𝜃] into ax-2
15772→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃Modus ponens 15770, 15771
15773→→⋀𝜑𝜒→→𝜒𝜃𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜒𝜃, 𝜒↗𝜃] into ax-2
15774→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15767, 15773
15775→→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15776→→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15774, 15775
15777→→→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→⋀𝜑𝜒→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
15778→→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15776, 15777
15779→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15768, 15778
15780→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀𝜑𝜒, 𝜒↗𝜃] into pm3.43
15781↔⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into df-an
15782→↔⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃] into bicom1
15783↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Modus ponens 15781, 15782
15784→↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃] into biimp
15785→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Modus ponens 15783, 15784
15786→→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃] into ax-1
15787→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15780, 15786
15788→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15789→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15787, 15788
15790→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15785, 15789
15791→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into pm3.2im
15792→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15793→→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15790, 15792
15794→→→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15795→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15793, 15794
15796→→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜓] into ax-1
15797→→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15795, 15796
15798→→→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15799→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15797, 15798
15800→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15791, 15799
15801→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃] into id
15802→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜓] into ax-1
15803→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15804→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Modus ponens 15802, 15803
15805→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃] into ax-2
15806→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃Modus ponens 15804, 15805
15807→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15808→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15800, 15807
15809→→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15810→→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15808, 15809
15811→→→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15812→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15810, 15811
15813→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15802, 15812
15814→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15815→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓Subs [𝜑↗→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
15816→→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓Modus ponens 15814, 15815
15817→→→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓] into ax-2
15818→→→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓Modus ponens 15816, 15817
15819→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓Modus ponens 15753, 15818
15820→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15821→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15813, 15820
15822→→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15823→→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15821, 15822
15824→→→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15825→→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15823, 15824
15826→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15819, 15825
15827→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
15828→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15829→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15827, 15828
15830→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
15831→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15829, 15830
15832→→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15833→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15826, 15832
15834→→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15835→→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15833, 15834
15836→→→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15837→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15835, 15836
15838→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15827, 15837
15839→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15840→→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
15841→→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓Modus ponens 15839, 15840
15842→→→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→𝜑𝜓] into ax-2
15843→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓Modus ponens 15841, 15842
15844→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15845→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15838, 15844
15846→→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15847→→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15845, 15846
15848→→→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15849→→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15847, 15848
15850↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into df-an
15851→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃] into notnotr
15852→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1
15853→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15827, 15852
15854→→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
15855→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15853, 15854
15856→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15851, 15855
15857→→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1
15858→¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15833, 15857
15859→→¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15860→→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15858, 15859
15861→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15856, 15860
15862→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1
15863→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
15864→→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓Modus ponens 15862, 15863
15865→→→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓] into ax-2
15866→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓Modus ponens 15864, 15865
15867→→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15868→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15861, 15867
15869→→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15870→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15868, 15869
15871→→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜒↗→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15872→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15870, 15871
15873→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15862, 15872
15874→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒⋀𝜓𝜃] into notnot
15875→→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1
15876→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15874, 15875
15877→→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15878→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15876, 15877
15879→→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15880→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15878, 15879
15881→→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15882→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15880, 15881
15883→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15873, 15882
15884→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-3
15885→→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
15886→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃Modus ponens 15884, 15885
15887→→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃] into ax-2
15888→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃Modus ponens 15886, 15887
15889→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃Modus ponens 15883, 15888
15890→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃] into id
15891→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15892→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15893→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15891, 15892
15894→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15895→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15893, 15894
15896→→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬→⋀𝜑𝜒𝜃] into ax-2
15897→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15889, 15896
15898→→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15899→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15897, 15898
15900→→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15901→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15899, 15900
15902→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15891, 15901
15903→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into id
15904→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15905→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15903, 15904
15906→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into notnotr
15907→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15908→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1
15909→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15907, 15908
15910→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15911→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15909, 15910
15912→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15906, 15911
15913→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15914→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15905, 15913
15915→→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1
15916→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15914, 15915
15917→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15918→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15916, 15917
15919→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1
15920→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15921→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15919, 15920
15922→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15923→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15921, 15922
15924→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15925→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15912, 15924
15926→→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15927→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15925, 15926
15928→→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15929→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15927, 15928
15930→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15919, 15929
15931→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-3
15932→→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15933→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15931, 15932
15934→→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15935→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15933, 15934
15936→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15930, 15935
15937→→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15938→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15936, 15937
15939→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15902, 15938
15940→→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-3
15941→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15939, 15940
15942→↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into biimp
15943→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 15850, 15942
15944→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-1
15945→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15941, 15944
15946→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15947→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15945, 15946
15948→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15943, 15947
15949→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15950→→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15827, 15949
15951→→→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
15952→→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15950, 15951
15953→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15779, 15952
15954↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into df-an
15955→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜒𝜃→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
15956→¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓Modus ponens 196, 15955
15957→→¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜒𝜃→𝜑𝜓] into ax-2
15958→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓Modus ponens 15956, 15957
15959→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓Modus ponens 532, 15958
15960→→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
15961→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15953, 15960
15962→→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1
15963→¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15961, 15962
15964→→¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2
15965→→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15963, 15964
15966→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15959, 15965
15967→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1
15968→→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃Subs [𝜑↗→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15969→→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃Modus ponens 15967, 15968
15970→→→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓→𝜒𝜃] into ax-2
15971→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃Modus ponens 15969, 15970
15972→→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
15973→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15966, 15972
15974→→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15975→→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15973, 15974
15976→→→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓→𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
15977→→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15975, 15976
15978→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15967, 15977
15979→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃] into notnot
15980→→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1
15981→¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃Modus ponens 15979, 15980
15982→→¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗¬¬→⋀𝜑𝜒𝜃] into ax-2
15983→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃Modus ponens 15981, 15982
15984→→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15985→→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃Modus ponens 15983, 15984
15986→→→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃] into ax-2
15987→→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃Modus ponens 15985, 15986
15988→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃Modus ponens 15978, 15987
15989→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-3
15990→→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓, 𝜓↗→𝜒𝜃] into ax-1
15991→→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓Modus ponens 15989, 15990
15992→→→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓] into ax-2
15993→→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓Modus ponens 15991, 15992
15994→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓Modus ponens 15988, 15993
15995→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃] into id
15996→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15997→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
15998→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃Modus ponens 15996, 15997
15999→→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜒𝜃¬→⋀𝜑𝜒𝜃] into ax-2
16000→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃Modus ponens 15998, 15999
16001→→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→𝜑𝜓] into ax-2
16002→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓Modus ponens 15994, 16001
16003→→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16004→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓Modus ponens 16002, 16003
16005→→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜒𝜃¬→𝜑𝜓] into ax-2
16006→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓Modus ponens 16004, 16005
16007→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓Modus ponens 15996, 16006
16008→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓] into id
16009→→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16010→¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16008, 16009
16011→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓] into notnotr
16012→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16013→→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1
16014→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16012, 16013
16015→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16016→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16014, 16015
16017→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16011, 16016
16018→→¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16019→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16010, 16018
16020→→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1
16021→¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16019, 16020
16022→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16023→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16021, 16022
16024→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1
16025→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16026→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 16024, 16025
16027→→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
16028→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 16026, 16027
16029→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16030→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16017, 16029
16031→→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16032→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16030, 16031
16033→→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16034→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16032, 16033
16035→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16024, 16034
16036→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗→→𝜒𝜃¬→𝜑𝜓] into ax-3
16037→→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16038→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16036, 16037
16039→→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16040→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16038, 16039
16041→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16035, 16040
16042→→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜒𝜃¬→𝜑𝜓, 𝜒↗¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16043→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16041, 16042
16044→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 16007, 16043
16045→→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-3
16046→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16044, 16045
16047→↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into biimp
16048→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Modus ponens 15954, 16047
16049→→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜒𝜃→𝜑𝜓] into ax-1
16050→⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16046, 16049
16051→→⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16052→→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16050, 16051
16053→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16048, 16052
16054→↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into bicom1
16055↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓Modus ponens 15954, 16054
16056→↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗⋀→𝜒𝜃→𝜑𝜓] into biimp
16057→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓Modus ponens 16055, 16056
16058→→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-1
16059→¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16053, 16058
16060→→¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃→→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗⋀→𝜒𝜃→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16061→→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16059, 16060
16062→→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into pm3.2im
16063→→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16064→→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16046, 16063
16065→→→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16066→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16064, 16065
16067→→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
16068→→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16066, 16067
16069→→→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
16070→→→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16068, 16069
16071→→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16072→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 15961, 16071
16073→→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2
16074→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16072, 16073
16075→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 196, 16074
16076↔⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into df-an
16077→¬¬→𝜒𝜃→𝜒𝜃Subs [𝜑↗→𝜒𝜃] into notnotr
16078→→𝜒𝜃→→𝜑𝜓→𝜒𝜃Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16079→→→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃Subs [𝜑↗→→𝜒𝜃→→𝜑𝜓→𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1
16080→¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃Modus ponens 16078, 16079
16081→→¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃→→¬¬→𝜒𝜃→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→→𝜑𝜓→𝜒𝜃] into ax-2
16082→→¬¬→𝜒𝜃→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃Modus ponens 16080, 16081
16083→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃Modus ponens 16077, 16082
16084→→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16085→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16075, 16084
16086→→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1
16087→¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16085, 16086
16088→→¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→→𝜑𝜓→𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
16089→→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16087, 16088
16090→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16083, 16089
16091→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜒𝜃] into ax-1
16092→→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
16093→→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓Modus ponens 16091, 16092
16094→→→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜒𝜃→𝜑𝜓] into ax-2
16095→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓Modus ponens 16093, 16094
16096→→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16097→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16090, 16096
16098→→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16099→→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16097, 16098
16100→→→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃→𝜑𝜓, 𝜒↗→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2
16101→→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16099, 16100
16102→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16091, 16101
16103→→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1
16104→¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃Modus ponens 15979, 16103
16105→→¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗¬¬→⋀𝜑𝜒𝜃] into ax-2
16106→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃Modus ponens 16104, 16105
16107→→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16108→→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃Modus ponens 16106, 16107
16109→→→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜒↗→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃] into ax-2
16110→→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃Modus ponens 16108, 16109
16111→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃Modus ponens 16102, 16110
16112→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃Subs [𝜑↗¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-3
16113→→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃Subs [𝜑↗→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16114→→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃Modus ponens 16112, 16113
16115→→→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃] into ax-2
16116→→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃Modus ponens 16114, 16115
16117→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃Modus ponens 16111, 16116
16118→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16119→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16120→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 16118, 16119
16121→→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
16122→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃Modus ponens 16120, 16121
16123→→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→𝜒𝜃] into ax-2
16124→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃Modus ponens 16117, 16123
16125→→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16126→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃Modus ponens 16124, 16125
16127→→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓¬→𝜒𝜃] into ax-2
16128→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃Modus ponens 16126, 16127
16129→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃Modus ponens 16118, 16128
16130→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃] into id
16131→→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16132→¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16130, 16131
16133→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃] into notnotr
16134→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16135→→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1
16136→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16134, 16135
16137→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16138→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16136, 16137
16139→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16133, 16138
16140→→¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16141→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16132, 16140
16142→→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1
16143→¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16141, 16142
16144→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16145→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16143, 16144
16146→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1
16147→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16148→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃Modus ponens 16146, 16147
16149→→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃] into ax-2
16150→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃Modus ponens 16148, 16149
16151→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16152→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16139, 16151
16153→→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16154→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16152, 16153
16155→→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16156→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16154, 16155
16157→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16146, 16156
16158→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗→→𝜑𝜓¬→𝜒𝜃] into ax-3
16159→→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16160→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16158, 16159
16161→→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16162→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16160, 16161
16163→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16157, 16162
16164→→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→𝜒𝜃, 𝜒↗¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16165→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16163, 16164
16166→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16129, 16165
16167→→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-3
16168→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16166, 16167
16169→↔⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃] into biimp
16170→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃Modus ponens 16076, 16169
16171→→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16172→⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16168, 16171
16173→→⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃→→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16174→→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16172, 16173
16175→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃Modus ponens 16170, 16174
16176→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into simpl
16177→↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into bicom1
16178↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15850, 16177
16179→↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃] into biimp
16180→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16178, 16179
16181→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1
16182→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15948, 16181
16183→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16184→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16182, 16183
16185→→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into pm3.2im
16186→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
16187→→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15941, 16186
16188→→→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16189→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16187, 16188
16190→→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
16191→→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16189, 16190
16192→→→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16193→→→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16191, 16192
16194→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16195→⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 15827, 16194
16196→→⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
16197→→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16195, 16196
16198→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃Modus ponens 16175, 16197
16199→→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16200→⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 15833, 16199
16201→→⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16202→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16200, 16201
16203→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16198, 16202
16204→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16205→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
16206→→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓Modus ponens 16204, 16205
16207→→→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓] into ax-2
16208→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓Modus ponens 16206, 16207
16209→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16210→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16203, 16209
16211→→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
16212→→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16210, 16211
16213→→→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16214→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16212, 16213
16215→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16204, 16214
16216→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16217→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16215, 16216
16218→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16219→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16217, 16218
16220→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16176, 16219
16221→⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃] into id
16222→→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16223→→⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16220, 16222
16224→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃Modus ponens 16221, 16223anim12
16225→→𝜓→𝜑𝜓→⋀𝜑𝜓→𝜓→𝜑𝜓Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
16226→⋀𝜑𝜓→𝜓→𝜑𝜓Modus ponens 208, 16225
16227→→⋀𝜑𝜓→𝜓→𝜑𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
16228→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜑𝜓Modus ponens 16226, 16227
16229→⋀𝜑𝜓→𝜑𝜓Modus ponens simpr, 16228pm3.4
16230↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑Subs [𝜓↗⋀𝜓𝜑] into bicom
16231↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜓↗⋀𝜓𝜒] into bicom
16232→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into id
16233→↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1
16234→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 7683, 16233
16235↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74
16236→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp
16237→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Modus ponens 16235, 16236
16238↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Modus ponens 16232, 16237
16239↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74
16240→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16241→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16239, 16240
16242↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16234, 16241
16243→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16244→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16242, 16243
16245→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp
16246→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Modus ponens 16238, 16245
16247→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1
16248→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16244, 16247
16249→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16250→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16248, 16249
16251→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16246, 16250
16252→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16253↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Modus ponens 16242, 16252
16254→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp
16255→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒Modus ponens 16253, 16254
16256→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into bicom1
16257↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16238, 16256
16258→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp
16259→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16257, 16258
16260→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16261→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16259, 16260
16262→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2
16263→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16261, 16262
16264→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16255, 16263
16265→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16266→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16251, 16265
16267↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16264, 16266
16268↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74
16269→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16270↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16268, 16269
16271→↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16272→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16270, 16271
16273→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16267, 16272
16274→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into id
16275→↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16276↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 7683, 16275
16277→↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16278→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16276, 16277
16279↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74
16280→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16281→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16279, 16280
16282↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16274, 16281
16283↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74
16284→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16285→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16283, 16284
16286↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16278, 16285
16287→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16288→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16286, 16287
16289→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16290→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16282, 16289
16291→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1
16292→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16288, 16291
16293→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2
16294→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16292, 16293
16295→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16290, 16294
16296→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1
16297↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16286, 16296
16298→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16299→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16297, 16298
16300→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16301↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16282, 16300
16302→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16303→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16301, 16302
16304→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1
16305→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16303, 16304
16306→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-2
16307→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16305, 16306
16308→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16299, 16307
16309→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into impbi
16310→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16295, 16309
16311↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16308, 16310
16312↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74
16313→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1
16314↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16312, 16313
16315→↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16316→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16314, 16315
16317→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16311, 16316
16318→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16319→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16273, 16318
16320↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16317, 16319
16321↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into bicom
16322→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into id
16323→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1
16324→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16231, 16323
16325↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74
16326→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16327→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16325, 16326
16328↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16322, 16327
16329↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74
16330→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16331→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16329, 16330
16332↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16324, 16331
16333→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16334→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16332, 16333
16335→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16336→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16328, 16335
16337→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16338→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16334, 16337
16339→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-2
16340→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16338, 16339
16341→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16336, 16340
16342→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1
16343↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16332, 16342
16344→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16345→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16343, 16344
16346→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into bicom1
16347↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16328, 16346
16348→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16349→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16347, 16348
16350→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-1
16351→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16349, 16350
16352→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16353→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16351, 16352
16354→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16345, 16353
16355→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into impbi
16356→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16341, 16355
16357↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16354, 16356
16358↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74
16359→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1
16360↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16358, 16359
16361→↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16362→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16360, 16361
16363→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16357, 16362
16364→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into id
16365→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜒𝜑] into bicom1
16366↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16231, 16365
16367→↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-1
16368→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16366, 16367
16369↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74
16370→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp
16371→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Modus ponens 16369, 16370
16372↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Modus ponens 16364, 16371
16373↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜒𝜑, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74
16374→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into biimp
16375→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16373, 16374
16376↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16368, 16375
16377→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into biimp
16378→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16376, 16377
16379→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp
16380→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Modus ponens 16372, 16379
16381→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16382→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16378, 16381
16383→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into ax-2
16384→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16382, 16383
16385→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16380, 16384
16386→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into bicom1
16387↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Modus ponens 16376, 16386
16388→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp
16389→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑Modus ponens 16387, 16388
16390→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into bicom1
16391↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16372, 16390
16392→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16393→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16391, 16392
16394→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into ax-1
16395→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16393, 16394
16396→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16397→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16395, 16396
16398→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16389, 16397
16399→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into impbi
16400→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16385, 16399
16401↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Modus ponens 16398, 16400
16402↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74
16403→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into bicom1
16404↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16402, 16403
16405→↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16406→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16404, 16405
16407→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16401, 16406
16408→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into impbi
16409→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16363, 16408
16410↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16407, 16409
16411↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜒𝜑] into bicom
16412→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16413→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16411, 16412
16414→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16415→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1
16416→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16413, 16415
16417→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16418→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16416, 16417
16419→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16363, 16418
16420→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16421↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16411, 16420
16422→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16423→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑Modus ponens 16421, 16422
16424→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1
16425↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16410, 16424
16426→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16427→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16428→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16407, 16427
16429→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜒↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-2
16430→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16428, 16429
16431→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16423, 16430
16432→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16433→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16419, 16432
16434↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16431, 16433
16435→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16436→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16437→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16321, 16436
16438→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16439→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16419, 16438
16440→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16441→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16439, 16440
16442→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16437, 16441
16443→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16444↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Modus ponens 16434, 16443
16445→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16446→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into bicom1
16447↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16321, 16446
16448→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16449→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16447, 16448
16450→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16451→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16449, 16450
16452→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16453→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16451, 16452
16454→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16431, 16453
16455→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16456→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16442, 16455
16457↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16454, 16456
16458→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16459→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16460→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1
16461→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16442, 16460
16462→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16463→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16461, 16462
16464→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16273, 16463
16465→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16466↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16457, 16465
16467→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16468→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16469↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16320, 16468
16470→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16471→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16472→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16317, 16471
16473→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2
16474→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16472, 16473
16475→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16454, 16474
16476→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16477→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16464, 16476
16478↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16475, 16477
16479↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into bicom
16480↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into biluk
16481→↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16482↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Modus ponens 16480, 16481
16483→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp
16484→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Modus ponens 16482, 16483
16485→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16486→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1
16487→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Modus ponens 16484, 16486
16488→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑𝜑] into ax-2
16489→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Modus ponens 16487, 16488
16490→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Modus ponens 16464, 16489
16491→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1
16492→↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16493→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒Modus ponens 16480, 16492
16494→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16495↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16478, 16494
16496→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16497→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into ax-1
16498→↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16475, 16497
16499→→↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2
16500→→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16498, 16499
16501→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16493, 16500
16502→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into impbi
16503→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Modus ponens 16490, 16502
16504↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Modus ponens 16501, 16503
16505→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp
16506→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16507→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16479, 16506
16508→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1
16509→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑Modus ponens 16490, 16508
16510→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑𝜑] into ax-2
16511→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Modus ponens 16509, 16510
16512→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Modus ponens 16507, 16511
16513→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1
16514↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Modus ponens 16504, 16513
16515→↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16516→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1
16517↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16479, 16516
16518→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp
16519→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16517, 16518
16520→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into ax-1
16521→↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16519, 16520
16522→→↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2
16523→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16521, 16522
16524→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16501, 16523
16525→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into impbi
16526→→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Modus ponens 16512, 16525
16527↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Modus ponens 16524, 16526
16528→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1
16529↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16527, 16528
16530→↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp
16531→↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp
16532→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑Modus ponens 16230, 16531
16533→→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1
16534→↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16524, 16533
16535→→↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2
16536→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16534, 16535
16537→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16532, 16536
16538→↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into bicom1
16539→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp
16540→↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1
16541↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑Modus ponens 16230, 16540
16542→↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp
16543→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑Modus ponens 16541, 16542
16544→→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑Subs [𝜑↗→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1
16545→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑Modus ponens 16543, 16544
16546→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑, 𝜒↗↔𝜑⋀𝜓𝜑] into ax-2
16547→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑Modus ponens 16545, 16546
16548→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑Modus ponens 16512, 16547
16549→→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into impbi
16550→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16537, 16549
16551↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16548, 16550
16552→↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp
16553→↔→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔𝜑⋀𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp
16554→→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
16555→→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16537, 16554
16556→→→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2
16557→→→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16555, 16556
16558→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 6441, 16557
16559→↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into bicom1
16560↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑Modus ponens 16551, 16559
16561→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp
16562→↔→𝜑𝜓↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into bicom1
16563↔↔𝜑⋀𝜓𝜑→𝜑𝜓Modus ponens pm4.71r, 16562
16564→↔↔𝜑⋀𝜓𝜑→𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into biimp
16565→→↔𝜑⋀𝜓𝜑→𝜑𝜓→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓Subs [𝜑↗→↔𝜑⋀𝜓𝜑→𝜑𝜓, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1
16566→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓Modus ponens 6452, 16565
16567→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2
16568→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 16566, 16567
16569→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓Modus ponens 16548, 16568
16570→→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into impbi
16571→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16558, 16570
16572↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒Modus ponens 16569, 16571biadan
16573→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into biimp
16574→→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓Subs [𝜑↗→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
16575→𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓Modus ponens 16573, 16574
16576→→𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜑↔𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓Subs [𝜓↗↔𝜓↔𝜑𝜓, 𝜒↗→𝜓↔𝜑𝜓] into ax-2
16577→→𝜑↔𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓Modus ponens 16575, 16576
16578→→𝜑→𝜓↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜒↗↔𝜑𝜓] into ax-2
16579→→→𝜑𝜓→𝜑↔𝜑𝜓→¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
16580→¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓Modus ponens 1697, 16579
16581→→¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑↔𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2
16582→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑↔𝜑𝜓Modus ponens 16580, 16581
16583→¬¬𝜓→𝜑↔𝜑𝜓Modus ponens 575, 16582
16584→→¬¬𝜓→𝜑↔𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16585→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓Modus ponens 16583, 16584
16586→→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
16587→𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓Modus ponens 16585, 16586
16588→→𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓↔𝜑𝜓Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓↔𝜑𝜓] into ax-2
16589→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓↔𝜑𝜓Modus ponens 16587, 16588
16590→𝜑→¬¬𝜓↔𝜑𝜓Modus ponens 581, 16589
16591→↔𝜑𝜓¬¬↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓] into notnot
16592→→↔𝜑𝜓¬¬↔𝜑𝜓→¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
16593→¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓Modus ponens 16591, 16592
16594→→¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2
16595→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓Modus ponens 16593, 16594
16596→→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓→𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓Subs [𝜑↗→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓, 𝜓↗𝜑] into ax-1
16597→𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓Modus ponens 16595, 16596
16598→→𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓→→𝜑→¬¬𝜓↔𝜑𝜓→𝜑→¬¬𝜓¬¬↔𝜑𝜓Subs [𝜓↗→¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬𝜓¬¬↔𝜑𝜓] into ax-2
16599→→𝜑→¬¬𝜓↔𝜑𝜓→𝜑→¬¬𝜓¬¬↔𝜑𝜓Modus ponens 16597, 16598
16600→𝜑→¬¬𝜓¬¬↔𝜑𝜓Modus ponens 16590, 16599
16601→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-3
16602→→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓→𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
16603→𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓Modus ponens 16601, 16602
16604→→𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓→→𝜑→¬¬𝜓¬¬↔𝜑𝜓→𝜑→¬↔𝜑𝜓¬𝜓Subs [𝜓↗→¬¬𝜓¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬𝜓] into ax-2
16605→→𝜑→¬¬𝜓¬¬↔𝜑𝜓→𝜑→¬↔𝜑𝜓¬𝜓Modus ponens 16603, 16604
16606→𝜑→¬↔𝜑𝜓¬𝜓Modus ponens 16600, 16605
16607→¬↔𝜑𝜓¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓] into id
16608→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗𝜑] into ax-1
16609→→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓Subs [𝜑↗→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16610→¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓Modus ponens 16608, 16609
16611→→¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→𝜑¬↔𝜑𝜓] into ax-2
16612→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓Modus ponens 16610, 16611
16613→→𝜑→¬↔𝜑𝜓¬𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓Subs [𝜓↗¬↔𝜑𝜓, 𝜒↗¬𝜓] into ax-2
16614→→𝜑¬↔𝜑𝜓→𝜑¬𝜓Modus ponens 16606, 16613
16615→→→𝜑¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓Subs [𝜑↗→→𝜑¬↔𝜑𝜓→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16616→¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓Modus ponens 16614, 16615
16617→→¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓→→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜑¬↔𝜑𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
16618→→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬𝜓Modus ponens 16616, 16617
16619→¬↔𝜑𝜓→𝜑¬𝜓Modus ponens 16608, 16618
16620→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16621→¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 619, 16620
16622→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16623→→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
16624→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Modus ponens 16622, 16623
16625→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→𝜑¬𝜓] into ax-2
16626→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Modus ponens 16624, 16625
16627→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Modus ponens 622, 16626
16628→→¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
16629→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Modus ponens 16621, 16628
16630→→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
16631→¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Modus ponens 16629, 16630
16632→→¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→𝜑¬𝜓] into ax-2
16633→→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓Modus ponens 16631, 16632
16634→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
16635→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16636→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓Modus ponens 16634, 16635
16637→→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓] into ax-2
16638→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓Modus ponens 16636, 16637
16639→→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
16640→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 16627, 16639
16641→→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16642→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 16640, 16641
16643→→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
16644→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 16642, 16643
16645→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓Modus ponens 16634, 16644
16646→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16647→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 647, 16646
16648→→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
16649→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 16647, 16648
16650→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓Modus ponens 16645, 16649
16651→→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓¬¬→𝜑¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
16652→→¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓¬¬→𝜑¬𝜓Modus ponens 16650, 16651
16653→¬↔𝜑𝜓¬¬→𝜑¬𝜓Modus ponens 16619, 16652
16654→→¬↔𝜑𝜓¬¬→𝜑¬𝜓→¬→𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-3
16655→¬→𝜑¬𝜓↔𝜑𝜓Modus ponens 16653, 16654
16656→→¬→𝜑¬𝜓↔𝜑𝜓→⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗→¬→𝜑¬𝜓↔𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
16657→⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓Modus ponens 16655, 16656
16658→→⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓↔𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16659→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓↔𝜑𝜓Modus ponens 16657, 16658
16660→⋀𝜑𝜓↔𝜑𝜓Modus ponens 4842, 16659pm5.1
16661↔⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into df-an
16662→¬¬¬𝜓¬𝜓Subs [𝜑↗¬𝜓] into notnotr
16663→¬𝜓→¬𝜑¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into ax-1
16664→→¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓Subs [𝜑↗→¬𝜓→¬𝜑¬𝜓, 𝜓↗¬¬¬𝜓] into ax-1
16665→¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓Modus ponens 16663, 16664
16666→→¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓→→¬¬¬𝜓¬𝜓→¬¬¬𝜓→¬𝜑¬𝜓Subs [𝜑↗¬¬¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2
16667→→¬¬¬𝜓¬𝜓→¬¬¬𝜓→¬𝜑¬𝜓Modus ponens 16665, 16666
16668→¬¬¬𝜓→¬𝜑¬𝜓Modus ponens 16662, 16667
16669→→¬𝜑→¬𝜓↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16670→→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗¬¬¬𝜓] into ax-1
16671→¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 3133, 16670
16672→→¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬¬¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜑↔𝜑𝜓Subs [𝜑↗¬¬¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2
16673→→¬¬¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 16671, 16672
16674→¬¬¬𝜓→¬𝜑↔𝜑𝜓Modus ponens 16668, 16673
16675→¬𝜑→¬¬¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬𝜓] into ax-1
16676→→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑Subs [𝜑↗→¬𝜑→¬¬¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
16677→¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑Modus ponens 16675, 16676
16678→→¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬𝜓¬𝜑] into ax-2
16679→→¬𝜑¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑Modus ponens 16677, 16678
16680→→¬¬¬𝜓→¬𝜑↔𝜑𝜓→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓Subs [𝜑↗¬¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16681→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓Modus ponens 16674, 16680
16682→→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓Subs [𝜑↗→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
16683→¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓Modus ponens 16681, 16682
16684→→¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓→→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬¬¬𝜓↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓¬𝜑, 𝜒↗→¬¬¬𝜓↔𝜑𝜓] into ax-2
16685→→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬¬¬𝜓↔𝜑𝜓Modus ponens 16683, 16684
16686→¬𝜑→¬¬¬𝜓↔𝜑𝜓Modus ponens 16675, 16685
16687→→↔𝜑𝜓¬¬↔𝜑𝜓→¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬¬¬𝜓] into ax-1
16688→¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓Modus ponens 16591, 16687
16689→→¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓Subs [𝜑↗¬¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2
16690→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓Modus ponens 16688, 16689
16691→→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓Subs [𝜑↗→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
16692→¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓Modus ponens 16690, 16691
16693→→¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓→→¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬¬𝜓¬¬↔𝜑𝜓] into ax-2
16694→→¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓Modus ponens 16692, 16693
16695→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓Modus ponens 16686, 16694
16696→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-3
16697→→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓→¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓Subs [𝜑↗→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1
16698→¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓Modus ponens 16696, 16697
16699→→¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓→→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→¬↔𝜑𝜓¬¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬¬𝜓] into ax-2
16700→→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→¬↔𝜑𝜓¬¬𝜓Modus ponens 16698, 16699
16701→¬𝜑→¬↔𝜑𝜓¬¬𝜓Modus ponens 16695, 16700
16702→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
16703→→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓Subs [𝜑↗→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16704→¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓Modus ponens 16702, 16703
16705→→¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬𝜑¬↔𝜑𝜓] into ax-2
16706→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓Modus ponens 16704, 16705
16707→→¬𝜑→¬↔𝜑𝜓¬¬𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬¬𝜓] into ax-2
16708→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓Modus ponens 16701, 16707
16709→→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓Subs [𝜑↗→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16710→¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓Modus ponens 16708, 16709
16711→→¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬𝜑¬↔𝜑𝜓, 𝜒↗→¬𝜑¬¬𝜓] into ax-2
16712→→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬¬𝜓Modus ponens 16710, 16711
16713→¬↔𝜑𝜓→¬𝜑¬¬𝜓Modus ponens 16702, 16712
16714→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬→¬𝜑¬¬𝜓] into id
16715→→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16716→¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Modus ponens 16714, 16715
16717→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬→¬𝜑¬¬𝜓] into notnotr
16718→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16719→→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1
16720→¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Modus ponens 16718, 16719
16721→→¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓] into ax-2
16722→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Modus ponens 16720, 16721
16723→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Modus ponens 16717, 16722
16724→→¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗¬→¬𝜑¬¬𝜓] into ax-2
16725→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Modus ponens 16716, 16724
16726→→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1
16727→¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Modus ponens 16725, 16726
16728→→¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓] into ax-2
16729→→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓Modus ponens 16727, 16728
16730→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1
16731→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓Subs [𝜑↗→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16732→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓Modus ponens 16730, 16731
16733→→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓] into ax-2
16734→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓Modus ponens 16732, 16733
16735→→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬→¬𝜑¬¬𝜓] into ax-2
16736→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Modus ponens 16723, 16735
16737→→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16738→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Modus ponens 16736, 16737
16739→→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓, 𝜒↗→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓] into ax-2
16740→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Modus ponens 16738, 16739
16741→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓Modus ponens 16730, 16740
16742→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓Subs [𝜑↗¬¬→¬𝜑¬¬𝜓, 𝜓↗→¬𝜑¬¬𝜓] into ax-3
16743→→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓Subs [𝜑↗→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16744→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓Modus ponens 16742, 16743
16745→→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜒↗→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓] into ax-2
16746→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓Modus ponens 16744, 16745
16747→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓Modus ponens 16741, 16746
16748→→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬𝜑¬¬𝜓, 𝜒↗¬¬→¬𝜑¬¬𝜓] into ax-2
16749→→¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓Modus ponens 16747, 16748
16750→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓Modus ponens 16713, 16749
16751→→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→¬𝜑¬¬𝜓] into ax-3
16752→¬→¬𝜑¬¬𝜓↔𝜑𝜓Modus ponens 16750, 16751
16753→↔⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓Subs [𝜑↗⋀¬𝜑¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓] into biimp
16754→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓Modus ponens 16661, 16753
16755→→¬→¬𝜑¬¬𝜓↔𝜑𝜓→⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓Subs [𝜑↗→¬→¬𝜑¬¬𝜓↔𝜑𝜓, 𝜓↗⋀¬𝜑¬𝜓] into ax-1
16756→⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓Modus ponens 16752, 16755
16757→→⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓→→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓↔𝜑𝜓Subs [𝜑↗⋀¬𝜑¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16758→→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓↔𝜑𝜓Modus ponens 16756, 16757
16759→⋀¬𝜑¬𝜓↔𝜑𝜓Modus ponens 16754, 16758pm5.21
16760→⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into pm5.1
16761→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into ax-1
16762→⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Modus ponens 1905, 16761
16763→→⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→→⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
16764→→⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Modus ponens 16762, 16763
16765→⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒Modus ponens 16760, 16764pm5.35
16766↔→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓Subs [𝜒↗→𝜑𝜓] into pm5.32
16767→↔→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓→→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓Subs [𝜑↗→𝜑↔𝜓→𝜑𝜓, 𝜓↗↔⋀𝜑𝜓⋀𝜑→𝜑𝜓] into biimp
16768→→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓Modus ponens 16766, 16767
16769↔⋀𝜑𝜓⋀𝜑→𝜑𝜓Modus ponens biimt, 16768abai
16770↔→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑Subs [𝜓↗→𝜓𝜑] into pm4.71
16771→↔→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑→→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗↔𝜑⋀𝜑→𝜓𝜑] into biimp
16772→→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑Modus ponens 16770, 16771
16773↔𝜑⋀𝜑→𝜓𝜑Modus ponens ax-1, 16772pm4.45im
16774→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into pm5.1
16775→↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into biimp
16776→→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
16777→↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑Modus ponens 16774, 16776
16778→→↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑, 𝜒↗↔→𝜑𝜓→𝜓𝜑] into ax-2
16779→→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑Modus ponens 16777, 16778
16780→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑Modus ponens 5712, 16779
16781→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1
16782→→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑Subs [𝜑↗→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
16783→¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑Modus ponens 16781, 16782
16784→→¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→→¬→𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓→𝜓𝜑] into ax-2
16785→→¬→𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑Modus ponens 16783, 16784
16786→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑Modus ponens pm2.521, 16785
16787→→𝜓𝜑¬¬→𝜓𝜑Subs [𝜑↗→𝜓𝜑] into notnot
16788→→→𝜓𝜑¬¬→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑Subs [𝜑↗→→𝜓𝜑¬¬→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1
16789→¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑Modus ponens 16787, 16788
16790→→¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗¬¬→𝜓𝜑] into ax-2
16791→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑Modus ponens 16789, 16790
16792→→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑Subs [𝜑↗→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
16793→¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑Modus ponens 16791, 16792
16794→→¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑→→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬↔𝜑𝜓→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓¬¬→𝜓𝜑] into ax-2
16795→→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑Modus ponens 16793, 16794
16796→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑Modus ponens 16786, 16795
16797→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-3
16798→→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
16799→¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓Modus ponens 16797, 16798
16800→→¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬↔𝜑𝜓¬¬→𝜓𝜑, 𝜒↗→¬→𝜓𝜑↔𝜑𝜓] into ax-2
16801→→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓Modus ponens 16799, 16800
16802→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓Modus ponens 16796, 16801
16803→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into biimpr
16804→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1
16805→→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Modus ponens 1674, 16804
16806→→→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2
16807→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑Modus ponens 16805, 16806
16808→→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1
16809→→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Modus ponens 1681, 16808
16810→→→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2
16811→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Modus ponens 16809, 16810
16812→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓Modus ponens 1674, 16811
16813→→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16814→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓Modus ponens 16812, 16813
16815→→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16816→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓Modus ponens 16814, 16815
16817→→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→→𝜓𝜑→𝜑𝜓, 𝜒↗→→𝜓𝜑↔𝜑𝜓] into ax-2
16818→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓Modus ponens 16816, 16817
16819→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓Modus ponens 16803, 16818
16820→↔→𝜑𝜓→𝜓𝜑→→𝜑𝜓→𝜓𝜑Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into biimp
16821→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16822→→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
16823→¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓Modus ponens 16821, 16822
16824→→¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓] into ax-2
16825→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓Modus ponens 16823, 16824
16826→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓Modus ponens 532, 16825
16827→→↔→𝜑𝜓→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓𝜑] into ax-2
16828→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑Modus ponens 16820, 16827
16829→→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑Subs [𝜑↗→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1
16830→¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑Modus ponens 16828, 16829
16831→→¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑] into ax-2
16832→→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑Modus ponens 16830, 16831
16833→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑Modus ponens 16826, 16832
16834→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑] into id
16835→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1
16836→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16837→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑Modus ponens 16835, 16836
16838→→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑] into ax-2
16839→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑Modus ponens 16837, 16838
16840→→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2
16841→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑Modus ponens 16833, 16840
16842→→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑Subs [𝜑↗→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16843→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑Modus ponens 16841, 16842
16844→→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓→𝜓𝜑] into ax-2
16845→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑Modus ponens 16843, 16844
16846→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑Modus ponens 16835, 16845
16847→→→𝜓𝜑¬¬→𝜓𝜑→¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑Subs [𝜑↗→→𝜓𝜑¬¬→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1
16848→¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑Modus ponens 16787, 16847
16849→→¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗¬¬→𝜓𝜑] into ax-2
16850→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑Modus ponens 16848, 16849
16851→→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑Subs [𝜑↗→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16852→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑Modus ponens 16850, 16851
16853→→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜓𝜑] into ax-2
16854→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑Modus ponens 16852, 16853
16855→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑Modus ponens 16846, 16854
16856→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-3
16857→→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16858→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓Modus ponens 16856, 16857
16859→→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜓𝜑, 𝜒↗→¬→𝜓𝜑¬→𝜑𝜓] into ax-2
16860→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓Modus ponens 16858, 16859
16861→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓Modus ponens 16855, 16860
16862→¬→𝜓𝜑¬→𝜓𝜑Subs [𝜑↗¬→𝜓𝜑] into id
16863→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
16864→→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→𝜓𝜑] into ax-1
16865→¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑Modus ponens 16863, 16864
16866→→¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→→¬→𝜓𝜑¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜓𝜑, 𝜒↗→¬→𝜑𝜓¬→𝜓𝜑] into ax-2
16867→→¬→𝜓𝜑¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑Modus ponens 16865, 16866
16868→→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16869→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓Modus ponens 16802, 16868
16870→→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓Subs [𝜑↗→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-1
16871→¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓Modus ponens 16869, 16870
16872→→¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓Subs [𝜑↗¬→𝜓𝜑, 𝜓↗→¬→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→𝜑𝜓↔𝜑𝜓] into ax-2
16873→→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓Modus ponens 16871, 16872
16874→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓Modus ponens 16863, 16873
16875→→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16876→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓Modus ponens 16874, 16875
16877→→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16878→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓Modus ponens 16876, 16877
16879→→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑¬→𝜑𝜓, 𝜒↗→¬→𝜓𝜑↔𝜑𝜓] into ax-2
16880→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓Modus ponens 16878, 16879
16881→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓Modus ponens 16861, 16880
16882→→↔𝜑𝜓¬¬↔𝜑𝜓→¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-1
16883→¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓Modus ponens 16591, 16882
16884→→¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓Subs [𝜑↗¬→𝜓𝜑, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2
16885→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓Modus ponens 16883, 16884
16886→→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓Subs [𝜑↗→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16887→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓Modus ponens 16885, 16886
16888→→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬→𝜓𝜑¬¬↔𝜑𝜓] into ax-2
16889→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓Modus ponens 16887, 16888
16890→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓Modus ponens 16881, 16889
16891→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑Subs [𝜑↗→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-3
16892→→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑Subs [𝜑↗→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16893→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑Modus ponens 16891, 16892
16894→→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓→𝜓𝜑] into ax-2
16895→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑Modus ponens 16893, 16894
16896→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑Modus ponens 16890, 16895
16897→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16898→→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16899→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓Modus ponens 16897, 16898
16900→→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓] into ax-2
16901→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓Modus ponens 16899, 16900
16902→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓Modus ponens 16819, 16901
16903→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16904→→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16905→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Modus ponens 16903, 16904
16906→→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜒↗→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓] into ax-2
16907→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Modus ponens 16905, 16906
16908→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Modus ponens 16902, 16907
16909→→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓↔𝜑𝜓] into ax-2
16910→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Modus ponens 16908, 16909
16911→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓Modus ponens 16896, 16910
16912→¬↔𝜑𝜓→↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔→𝜑𝜓→𝜓𝜑] into pm2.21
16913→→¬↔𝜑𝜓→↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬↔→𝜑𝜓→𝜓𝜑] into ax-2
16914→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑Modus ponens 16912, 16913
16915→→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16916→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑Modus ponens 16914, 16915
16917→→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑] into ax-2
16918→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑Modus ponens 16916, 16917
16919→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑Modus ponens 16911, 16918
16920→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-3
16921→→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Subs [𝜑↗→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16922→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens 16920, 16921
16923→→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑, 𝜒↗→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓] into ax-2
16924→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens 16922, 16923
16925→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens 16919, 16924
16926→→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16927→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens 16925, 16926
16928→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓Modus ponens 16834, 16927
16929→→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into impbi
16930→→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑Modus ponens 16780, 16929
16931↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑Modus ponens 16928, 16930impimprbi
16932↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒Subs [𝜒↗¬𝜒] into impexp
16933↔→𝜓¬𝜒¬⋀𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒] into imnan
16934→↔→𝜓¬𝜒¬⋀𝜓𝜒→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒Subs [𝜑↗↔→𝜓¬𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
16935→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒Modus ponens 16933, 16934
16936↔→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜓↗→𝜓¬𝜒, 𝜒↗¬⋀𝜓𝜒] into pm5.74
16937→↔→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒, 𝜓↗↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒] into biimp
16938→→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 16936, 16937
16939↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 16935, 16938
16940→↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp
16941→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 16939, 16940
16942→↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into biimp
16943→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒Modus ponens 16932, 16942
16944→→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-1
16945→→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 16941, 16944
16946→→→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
16947→→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 16945, 16946
16948→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 16943, 16947
16949→↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1
16950↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒Modus ponens 16939, 16949
16951→↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into biimp
16952→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒Modus ponens 16950, 16951
16953→↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into bicom1
16954↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒Modus ponens 16932, 16953
16955→↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into biimp
16956→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒Modus ponens 16954, 16955
16957→→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into ax-1
16958→→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒Modus ponens 16956, 16957
16959→→→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑→𝜓¬𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
16960→→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Modus ponens 16958, 16959
16961→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Modus ponens 16952, 16960
16962→→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into impbi
16963→→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 16948, 16962
16964↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒Modus ponens 16961, 16963
16965→↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1
16966↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Modus ponens 16964, 16965nan
16967→⋀𝜒→𝜑𝜓→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into simpr
16968→⋀𝜒→𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into simpl
16969→→𝜒→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
16970→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒Modus ponens 1834, 16969
16971→→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑𝜒Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
16972→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑𝜒Modus ponens 16970, 16971
16973→⋀𝜒→𝜑𝜓→𝜑𝜒Modus ponens 16968, 16972
16974→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Subs [𝜑↗→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
16975→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Modus ponens 5594, 16974
16976→→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜓𝜒] into ax-2
16977→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Modus ponens 16975, 16976
16978→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒Modus ponens 16967, 16977
16979→→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
16980→⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 5595, 16979
16981→→⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2
16982→→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 16980, 16981
16983→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒Modus ponens 16978, 16982
16984→→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
16985→→⋀𝜒→𝜑𝜓→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 16983, 16984
16986→⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒Modus ponens 16973, 16985pm5.31
16987→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜓↗𝜒, 𝜒↗𝜓] into pm3.43
16988↔⋀→𝜑𝜒→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into df-an
16989→↔⋀→𝜑𝜒→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓Subs [𝜑↗⋀→𝜑𝜒→𝜑𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓] into bicom1
16990↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓Modus ponens 16988, 16989
16991→↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓Subs [𝜑↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜓↗⋀→𝜑𝜒→𝜑𝜓] into biimp
16992→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓Modus ponens 16990, 16991
16993→→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓] into ax-1
16994→¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 16987, 16993
16995→→¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜓↗⋀→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
16996→→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 16994, 16995
16997→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 16992, 16996
16998→→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into pm3.2im
16999→→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
17000→→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 16997, 16999
17001→→→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17002→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17000, 17001
17003→→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜒] into ax-1
17004→→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17002, 17003
17005→→→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17006→→→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17004, 17005
17007→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 16998, 17006
17008→→𝜑𝜓→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into ax-1
17009→→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17010→→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓Modus ponens 17008, 17009
17011→→→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑𝜒→𝜑𝜓] into ax-2
17012→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓Modus ponens 17010, 17011
17013→→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17014→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓Modus ponens 17007, 17013
17015→→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
17016→→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓Modus ponens 17014, 17015
17017→→→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗→→𝜑𝜒→𝜑⋀𝜒𝜓] into ax-2
17018→→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓Modus ponens 17016, 17017
17019→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓Modus ponens 17008, 17018
17020→→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗𝜒] into ax-1
17021→𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 5603, 17020
17022→→𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→→𝜑𝜓→𝜑𝜒Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
17023→→𝜒→𝜑𝜒→𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 17021, 17022
17024→𝜒→→𝜑𝜓→𝜑𝜒Modus ponens 1834, 17023
17025→→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17026→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17019, 17025
17027→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17028→𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17026, 17027
17029→→𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17030→→𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17028, 17029
17031→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17024, 17030
17032→→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17033→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17031, 17032
17034→→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
17035→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17033, 17034
17036→→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2
17037→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17035, 17036
17038→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 39, 17037
17039→→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17040→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17038, 17039
17041→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17042→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17040, 17041
17043→→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17044→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17042, 17043
17045↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into df-an
17046→→→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17047→¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 39, 17046
17048→→¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2
17049→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 17047, 17048
17050→¬¬→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 532, 17049
17051→→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17052→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17033, 17051
17053→→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2
17054→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17052, 17053
17055→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17050, 17054
17056→𝜒→¬¬→𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1
17057→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→𝜒→¬¬→𝜑𝜓𝜒Subs [𝜑↗→𝜒→¬¬→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
17058→𝜒→𝜒→¬¬→𝜑𝜓𝜒Modus ponens 17056, 17057
17059→→𝜒→𝜒→¬¬→𝜑𝜓𝜒→→𝜒𝜒→𝜒→¬¬→𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→¬¬→𝜑𝜓𝜒] into ax-2
17060→→𝜒𝜒→𝜒→¬¬→𝜑𝜓𝜒Modus ponens 17058, 17059
17061→→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17062→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17055, 17061
17063→→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17064→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17062, 17063
17065→→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17066→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17064, 17065
17067→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17056, 17066
17068→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑⋀𝜒𝜓] into notnot
17069→→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓Subs [𝜑↗→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17070→¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓Modus ponens 17068, 17069
17071→→¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑⋀𝜒𝜓, 𝜒↗¬¬→𝜑⋀𝜒𝜓] into ax-2
17072→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓Modus ponens 17070, 17071
17073→→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17074→𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓Modus ponens 17072, 17073
17075→→𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓] into ax-2
17076→→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓Modus ponens 17074, 17075
17077→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓Modus ponens 17067, 17076
17078→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-3
17079→→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓, 𝜓↗𝜒] into ax-1
17080→𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓Modus ponens 17078, 17079
17081→→𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓] into ax-2
17082→→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓Modus ponens 17080, 17081
17083→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓Modus ponens 17077, 17082
17084→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓] into id
17085→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17086→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓Subs [𝜑↗→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17087→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓Modus ponens 17085, 17086
17088→→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗→𝜒¬→𝜑⋀𝜒𝜓] into ax-2
17089→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓Modus ponens 17087, 17088
17090→→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
17091→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓Modus ponens 17083, 17090
17092→→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17093→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓Modus ponens 17091, 17092
17094→→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→𝜒¬→𝜑⋀𝜒𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2
17095→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓Modus ponens 17093, 17094
17096→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓Modus ponens 17085, 17095
17097→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜒¬→𝜑𝜓] into id
17098→→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17099→¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17097, 17098
17100→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜒¬→𝜑𝜓] into notnotr
17101→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17102→→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17103→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17101, 17102
17104→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17105→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17103, 17104
17106→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17100, 17105
17107→→¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2
17108→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17099, 17107
17109→→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17110→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17108, 17109
17111→→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17112→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17110, 17111
17113→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17114→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓Subs [𝜑↗→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17115→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓Modus ponens 17113, 17114
17116→→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓] into ax-2
17117→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓Modus ponens 17115, 17116
17118→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2
17119→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17106, 17118
17120→→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17121→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17119, 17120
17122→→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17123→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17121, 17122
17124→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17113, 17123
17125→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬¬→𝜒¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓] into ax-3
17126→→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17127→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17125, 17126
17128→→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓] into ax-2
17129→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17127, 17128
17130→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17124, 17129
17131→→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗¬¬→𝜒¬→𝜑𝜓] into ax-2
17132→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17130, 17131
17133→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17096, 17132
17134→→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-3
17135→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17133, 17134
17136→↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into biimp
17137→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17045, 17136
17138→→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17139→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17135, 17138
17140→→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17141→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17139, 17140
17142→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17137, 17141pm5.31r
17143↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into df-an
17144→→𝜒→→𝜑𝜓𝜒→¬¬𝜒→𝜒→→𝜑𝜓𝜒Subs [𝜑↗→𝜒→→𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
17145→¬¬𝜒→𝜒→→𝜑𝜓𝜒Modus ponens 7185, 17144
17146→→¬¬𝜒→𝜒→→𝜑𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→→𝜑𝜓𝜒Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓𝜒] into ax-2
17147→→¬¬𝜒𝜒→¬¬𝜒→→𝜑𝜓𝜒Modus ponens 17145, 17146
17148→¬¬𝜒→→𝜑𝜓𝜒Modus ponens 5153, 17147
17149→→→𝜑𝜓→𝜒→𝜑𝜓→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜓] into ax-2
17150→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓Modus ponens 39, 17149
17151→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1
17152→¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓Modus ponens 17150, 17151
17153→→¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→→¬¬𝜒→→𝜑𝜓𝜒→¬¬𝜒→→𝜑𝜓→𝜑𝜓Subs [𝜑↗¬¬𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜓] into ax-2
17154→→¬¬𝜒→→𝜑𝜓𝜒→¬¬𝜒→→𝜑𝜓→𝜑𝜓Modus ponens 17152, 17153
17155→¬¬𝜒→→𝜑𝜓→𝜑𝜓Modus ponens 17148, 17154
17156→→𝜑𝜓→¬¬𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1
17157→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→¬¬𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17158→→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓Modus ponens 17156, 17157
17159→→→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬𝜒→𝜑𝜓] into ax-2
17160→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓Modus ponens 17158, 17159
17161→→¬¬𝜒→→𝜑𝜓→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17162→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓Modus ponens 17155, 17161
17163→→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓Subs [𝜑↗→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17164→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓Modus ponens 17162, 17163
17165→→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒→𝜑𝜓, 𝜒↗→¬¬𝜒→𝜑𝜓] into ax-2
17166→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓Modus ponens 17164, 17165
17167→→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗→𝜑𝜓] into notnot
17168→→→𝜑𝜓¬¬→𝜑𝜓→¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1
17169→¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓Modus ponens 17167, 17168
17170→→¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
17171→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓Modus ponens 17169, 17170
17172→→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓Subs [𝜑↗→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17173→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓Modus ponens 17171, 17172
17174→→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒→𝜑𝜓, 𝜒↗→¬¬𝜒¬¬→𝜑𝜓] into ax-2
17175→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓Modus ponens 17173, 17174
17176→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓Modus ponens 17156, 17175
17177→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-3
17178→→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒→→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒, 𝜓↗→𝜑𝜓] into ax-1
17179→→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒Modus ponens 17177, 17178
17180→→→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒→→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→¬→𝜑𝜓¬𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬𝜒] into ax-2
17181→→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→¬→𝜑𝜓¬𝜒Modus ponens 17179, 17180
17182→→𝜑𝜓→¬→𝜑𝜓¬𝜒Modus ponens 17176, 17181
17183→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17184→→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17185→¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓Modus ponens 17183, 17184
17186→→¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬→𝜑𝜓] into ax-2
17187→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓Modus ponens 17185, 17186
17188→→→𝜑𝜓→¬→𝜑𝜓¬𝜒→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬𝜒] into ax-2
17189→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒Modus ponens 17182, 17188
17190→→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒Subs [𝜑↗→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17191→¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒Modus ponens 17189, 17190
17192→→¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬𝜒Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬𝜒] into ax-2
17193→→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬𝜒Modus ponens 17191, 17192
17194→¬→𝜑𝜓→→𝜑𝜓¬𝜒Modus ponens 17183, 17193
17195→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬→→𝜑𝜓¬𝜒] into id
17196→→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17197→¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Modus ponens 17195, 17196
17198→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬→→𝜑𝜓¬𝜒] into notnotr
17199→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17200→→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1
17201→¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Modus ponens 17199, 17200
17202→→¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒] into ax-2
17203→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Modus ponens 17201, 17202
17204→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Modus ponens 17198, 17203
17205→→¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗¬→→𝜑𝜓¬𝜒] into ax-2
17206→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Modus ponens 17197, 17205
17207→→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Subs [𝜑↗→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1
17208→¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Modus ponens 17206, 17207
17209→→¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜒↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒] into ax-2
17210→→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒Modus ponens 17208, 17209
17211→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1
17212→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17213→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓Modus ponens 17211, 17212
17214→→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓] into ax-2
17215→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓Modus ponens 17213, 17214
17216→→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→→𝜑𝜓¬𝜒] into ax-2
17217→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Modus ponens 17204, 17216
17218→→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17219→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Modus ponens 17217, 17218
17220→→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓, 𝜒↗→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒] into ax-2
17221→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Modus ponens 17219, 17220
17222→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒Modus ponens 17211, 17221
17223→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬¬→→𝜑𝜓¬𝜒, 𝜓↗→→𝜑𝜓¬𝜒] into ax-3
17224→→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17225→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒Modus ponens 17223, 17224
17226→→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜒↗→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒] into ax-2
17227→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒Modus ponens 17225, 17226
17228→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒Modus ponens 17222, 17227
17229→→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→→𝜑𝜓¬𝜒, 𝜒↗¬¬→→𝜑𝜓¬𝜒] into ax-2
17230→→¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒Modus ponens 17228, 17229
17231→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒Modus ponens 17194, 17230
17232→→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒] into ax-3
17233→¬→→𝜑𝜓¬𝜒→𝜑𝜓Modus ponens 17231, 17232
17234→↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒] into biimp
17235→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒Modus ponens 17143, 17234
17236→→¬→→𝜑𝜓¬𝜒→𝜑𝜓→⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→𝜑𝜓, 𝜓↗⋀→𝜑𝜓𝜒] into ax-1
17237→⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓Modus ponens 17233, 17236
17238→→⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓→→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜑𝜓] into ax-2
17239→→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓Modus ponens 17237, 17238
17240→⋀→𝜑𝜓𝜒→𝜑𝜓Modus ponens 17235, 17239
17241→↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒] into bicom1
17242↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒Modus ponens 17143, 17241
17243→↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗⋀→𝜑𝜓𝜒] into biimp
17244→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒Modus ponens 17242, 17243
17245→→⋀→𝜑𝜓𝜒→𝜑𝜓→¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓Subs [𝜑↗→⋀→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒] into ax-1
17246→¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓Modus ponens 17240, 17245
17247→→¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓→→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗⋀→𝜑𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
17248→→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓Modus ponens 17246, 17247
17249→→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into pm3.2im
17250→→¬→→𝜑𝜓¬𝜒→𝜑𝜓→𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→𝜑𝜓, 𝜓↗𝜒] into ax-1
17251→𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓Modus ponens 17233, 17250
17252→→𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜑𝜓] into ax-2
17253→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓Modus ponens 17251, 17252
17254→→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓Subs [𝜑↗→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17255→→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓Modus ponens 17253, 17254
17256→→→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓→→→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒→→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜒→𝜑𝜓] into ax-2
17257→→→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒→→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 17255, 17256
17258→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓, 𝜓↗𝜒] into ax-1
17259→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓Modus ponens 17150, 17258
17260→→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜓] into ax-2
17261→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑𝜓Modus ponens 17259, 17260
17262→𝜒→→𝜑𝜓→𝜑𝜓Modus ponens 7185, 17261
17263→→𝜒→→𝜑𝜓→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17264→→𝜒→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 17262, 17263
17265→→→𝜒→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17266→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 17264, 17265
17267→→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2
17268→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 17266, 17267
17269→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜓] into ax-2
17270→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓Modus ponens 17050, 17269
17271→→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓Subs [𝜑↗→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓, 𝜓↗𝜒] into ax-1
17272→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓Modus ponens 17270, 17271
17273→→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑𝜓] into ax-2
17274→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑𝜓Modus ponens 17272, 17273
17275→𝜒→¬¬→𝜑𝜓→𝜑𝜓Modus ponens 17056, 17274
17276→→→𝜑𝜓¬¬→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17277→¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓Modus ponens 17167, 17276
17278→→¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
17279→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓Modus ponens 17277, 17278
17280→→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗𝜒] into ax-1
17281→𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓Modus ponens 17279, 17280
17282→→𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑𝜓] into ax-2
17283→→𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓Modus ponens 17281, 17282
17284→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓Modus ponens 17275, 17283
17285→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-3
17286→→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗𝜒] into ax-1
17287→𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓Modus ponens 17285, 17286
17288→→𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜑𝜓] into ax-2
17289→→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→¬→𝜑𝜓¬→𝜑𝜓Modus ponens 17287, 17288
17290→𝜒→¬→𝜑𝜓¬→𝜑𝜓Modus ponens 17284, 17289
17291→¬→𝜑𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜒] into ax-1
17292→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17293→¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓Modus ponens 17291, 17292
17294→→¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2
17295→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓Modus ponens 17293, 17294
17296→→𝜒→¬→𝜑𝜓¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
17297→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓Modus ponens 17290, 17296
17298→→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17299→¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓Modus ponens 17297, 17298
17300→→¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2
17301→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓Modus ponens 17299, 17300
17302→→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17303→¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17097, 17302
17304→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17305→→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17306→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17304, 17305
17307→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17308→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17306, 17307
17309→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17100, 17308
17310→→¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2
17311→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17303, 17310
17312→→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17313→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17311, 17312
17314→→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17315→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17313, 17314
17316→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17317→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17318→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓Modus ponens 17316, 17317
17319→→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓] into ax-2
17320→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓Modus ponens 17318, 17319
17321→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2
17322→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17309, 17321
17323→→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17324→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17322, 17323
17325→→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17326→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17324, 17325
17327→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓Modus ponens 17316, 17326
17328→→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17329→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17125, 17328
17330→→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓] into ax-2
17331→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17329, 17330
17332→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17327, 17331
17333→→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗¬¬→𝜒¬→𝜑𝜓] into ax-2
17334→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17332, 17333
17335→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓Modus ponens 17291, 17334
17336→→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-3
17337→¬→𝜒¬→𝜑𝜓→𝜑𝜓Modus ponens 17335, 17336
17338→→¬→𝜒¬→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17339→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓Modus ponens 17337, 17338
17340→→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17341→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑𝜓Modus ponens 17339, 17340
17342→↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into bicom1
17343↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓Modus ponens 17045, 17342
17344→↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into biimp
17345→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓Modus ponens 17343, 17344
17346→→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-1
17347→¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens pm5.31r, 17346
17348→→¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17349→→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17347, 17348
17350→𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into pm3.2im
17351→→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
17352→→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17135, 17351
17353→→→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17354→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17352, 17353
17355→→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17356→𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17354, 17355
17357→→𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17358→→𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17356, 17357
17359→→→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17360→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 39, 17359
17361→→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2
17362→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 17360, 17361
17363→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓Modus ponens 16967, 17362
17364→→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17365→⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17033, 17364
17366→→⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2
17367→→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17365, 17366
17368→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓Modus ponens 17363, 17367
17369→𝜒→⋀𝜒→𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17370→→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒Subs [𝜑↗→𝜒→⋀𝜒→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
17371→𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒Modus ponens 17369, 17370
17372→→𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒→→𝜒𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜒→𝜑𝜓𝜒] into ax-2
17373→→𝜒𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒Modus ponens 17371, 17372
17374→→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17375→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17368, 17374
17376→→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17377→𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17375, 17376
17378→→𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗𝜒, 𝜓↗→⋀𝜒→𝜑𝜓𝜒, 𝜒↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17379→→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17377, 17378
17380→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17369, 17379
17381→→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17382→⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17380, 17381
17383→→⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17384→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17382, 17383
17385→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 16968, 17384
17386→⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓] into id
17387→→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17388→→⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓Modus ponens 17385, 17387
17389↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into con2b
17390→↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into biimp
17391→↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp
17392→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒Modus ponens 17389, 17391
17393→→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑] into ax-1
17394→→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒Modus ponens 16961, 17393
17395→→→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
17396→→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒Modus ponens 17394, 17395
17397→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒Modus ponens 17392, 17396
17398→↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into bicom1
17399→↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp
17400→↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1
17401↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑Modus ponens 17389, 17400
17402→↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑] into biimp
17403→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑Modus ponens 17401, 17402
17404→→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-1
17405→→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑Modus ponens 17403, 17404
17406→→→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2
17407→→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑Modus ponens 17405, 17406
17408→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑Modus ponens 16948, 17407
17409→→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒→→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into impbi
17410→→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒Modus ponens 17397, 17409
17411↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒Modus ponens 17408, 17410
17412→↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into bicom1
17413↔→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑Modus ponens 17411, 17412pm4.15
17414↔→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.32
17415→↔→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓] into biimp
17416→→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓Modus ponens 17414, 17415
17417↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓Modus ponens 1651, 17416
17418↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑Subs [𝜓↗↔𝜑𝜓] into ancom
17419↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into ancom
17420→↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓] into bicom1
17421↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓Modus ponens 17419, 17420
17422→↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into biimp
17423→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓Modus ponens 17421, 17422
17424→↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓] into biimp
17425→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓Modus ponens 17417, 17424
17426→→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into ax-1
17427→⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓Modus ponens 17423, 17426
17428→→⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓, 𝜒↗⋀𝜓↔𝜑𝜓] into ax-2
17429→→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Modus ponens 17427, 17428
17430→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Modus ponens 17425, 17429
17431→↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into bicom1
17432→↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓] into biimp
17433→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓Modus ponens 17419, 17432
17434→↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓] into bicom1
17435↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑Modus ponens 17417, 17434
17436→↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp
17437→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑Modus ponens 17435, 17436
17438→→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑Subs [𝜑↗→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into ax-1
17439→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑Modus ponens 17437, 17438
17440→→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓, 𝜒↗⋀↔𝜑𝜓𝜑] into ax-2
17441→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑Modus ponens 17439, 17440
17442→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑Modus ponens 17433, 17441
17443→→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into impbi
17444→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Modus ponens 17430, 17443
17445↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Modus ponens 17442, 17444
17446→↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into biimp
17447→↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp
17448→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑Modus ponens 17418, 17447
17449→→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓, 𝜓↗⋀𝜑↔𝜑𝜓] into ax-1
17450→⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓Modus ponens 17430, 17449
17451→→⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑, 𝜒↗⋀𝜓↔𝜑𝜓] into ax-2
17452→→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓Modus ponens 17450, 17451
17453→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓Modus ponens 17448, 17452
17454→↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into bicom1
17455↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑Modus ponens 17445, 17454
17456→↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp
17457→↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into bicom1
17458↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓Modus ponens 17418, 17457
17459→↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜑↔𝜑𝜓] into biimp
17460→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓Modus ponens 17458, 17459
17461→→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓Subs [𝜑↗→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into ax-1
17462→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓Modus ponens 17460, 17461
17463→→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑, 𝜒↗⋀𝜑↔𝜑𝜓] into ax-2
17464→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓Modus ponens 17462, 17463
17465→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓Modus ponens 17442, 17464
17466→→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into impbi
17467→→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓Modus ponens 17453, 17466
17468↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓Modus ponens 17465, 17467pm5.36
17469↔⋀𝜑𝜓¬¬⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓] into notnotb
17470→↔⋀𝜑𝜓¬¬⋀𝜑𝜓↔¬¬⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬⋀𝜑𝜓] into bicom1
17471↔¬¬⋀𝜑𝜓⋀𝜑𝜓Modus ponens 17469, 17470
17472→↔¬¬⋀𝜑𝜓⋀𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓Subs [𝜑↗↔¬¬⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17473→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓Modus ponens 17471, 17472
17474↔→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗⋀𝜑𝜓] into pm5.74
17475→↔→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓] into biimp
17476→→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 17474, 17475
17477↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 17473, 17476
17478↔→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into pm5.74
17479→↔→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑↔⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑⋀𝜑𝜓→𝜑𝜓] into biimp
17480→→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 17478, 17479
17481→↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
17482→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 17477, 17481
17483→→→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into ax-1
17484→→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 6193, 17483
17485→→→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17486→→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Modus ponens 17484, 17485
17487→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Modus ponens 17482, 17486
17488→↔→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1
17489→↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1
17490↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17477, 17489
17491→↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into biimp
17492→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17490, 17491
17493→→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17494→→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17492, 17493
17495→→→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2
17496→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17494, 17495
17497→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens ancl, 17496
17498→→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into impbi
17499→→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Modus ponens 17487, 17498
17500↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Modus ponens 17497, 17499
17501↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗𝜓] into pm5.74
17502→↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓] into bicom1
17503↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓Modus ponens 17501, 17502
17504→↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓Subs [𝜑↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑↔¬¬⋀𝜑𝜓𝜓] into biimp
17505→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓Modus ponens 17503, 17504
17506→𝜑↔¬¬⋀𝜑𝜓𝜓Modus ponens 17500, 17505
17507→↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓] into biimp
17508→→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Modus ponens 17501, 17507
17509→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp
17510→→→𝜑𝜓→𝜑¬¬𝜓→→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓Subs [𝜑↗→→𝜑𝜓→𝜑¬¬𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into ax-1
17511→→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓Modus ponens 4585, 17510
17512→→→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓→→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬¬𝜓] into ax-2
17513→→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓Modus ponens 17511, 17512
17514→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓Modus ponens 17487, 17513
17515→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1
17516↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17500, 17515
17517→↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into biimp
17518→→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into ax-1
17519→→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17497, 17518
17520→→→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2
17521→→→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17519, 17520
17522→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 4598, 17521
17523→→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into impbi
17524→→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓Modus ponens 17514, 17523
17525↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓Modus ponens 17522, 17524
17526↔→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74
17527→↔→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓] into bicom1
17528↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓Modus ponens 17526, 17527
17529→↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓Subs [𝜑↗↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓, 𝜓↗→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓] into biimp
17530→↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓Modus ponens 17528, 17529
17531→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓Modus ponens 17525, 17530
17532↔↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜑↗¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into bicom
17533→↔↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜑↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗↔¬¬𝜓¬¬⋀𝜑𝜓] into biimp
17534→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17532, 17533
17535→→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜑↗→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17536→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17534, 17535
17537→→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜓↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗↔¬¬𝜓¬¬⋀𝜑𝜓] into ax-2
17538→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17536, 17537
17539→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17531, 17538
17540→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬⋀𝜑𝜓] into biimp
17541→→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜑↗→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17542→𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17540, 17541
17543→→𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜓↗↔¬¬𝜓¬¬⋀𝜑𝜓, 𝜒↗→¬¬𝜓¬¬⋀𝜑𝜓] into ax-2
17544→→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17542, 17543
17545→𝜑→¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17539, 17544
17546→¬¬𝜓→𝜑¬¬𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑] into ax-1
17547→→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓Subs [𝜑↗→¬¬𝜓→𝜑¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1
17548→¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓Modus ponens 17546, 17547
17549→→¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓→→¬¬𝜓¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗→𝜑¬¬𝜓] into ax-2
17550→→¬¬𝜓¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓Modus ponens 17548, 17549
17551→→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜓↗¬¬𝜓, 𝜒↗¬¬⋀𝜑𝜓] into ax-2
17552→→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓→¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
17553→¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17522, 17552
17554→→¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓→→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→𝜑¬¬⋀𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2
17555→→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17553, 17554
17556→¬¬𝜓→𝜑¬¬⋀𝜑𝜓Modus ponens 17546, 17555
17557→→¬¬𝜓→𝜑¬¬⋀𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗¬¬⋀𝜑𝜓] into ax-2
17558→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17556, 17557
17559→→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17560→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17558, 17559
17561→→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜑𝜓Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓¬¬⋀𝜑𝜓] into ax-2
17562→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜑𝜓Modus ponens 17560, 17561
17563→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓Subs [𝜑↗¬𝜓, 𝜓↗¬⋀𝜑𝜓] into ax-3
17564→→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓→𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17565→𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓Modus ponens 17563, 17564
17566→→𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓→→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬⋀𝜑𝜓¬𝜓Subs [𝜓↗→¬¬𝜓¬¬⋀𝜑𝜓, 𝜒↗→¬⋀𝜑𝜓¬𝜓] into ax-2
17567→→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬⋀𝜑𝜓¬𝜓Modus ponens 17565, 17566
17568→𝜑→¬⋀𝜑𝜓¬𝜓Modus ponens 17545, 17567
17569→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓Subs [𝜑↗¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into biimp
17570→→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓Subs [𝜑↗→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1
17571→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓Modus ponens 17569, 17570
17572→→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬¬⋀𝜑𝜓¬¬𝜓Subs [𝜓↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗→¬¬⋀𝜑𝜓¬¬𝜓] into ax-2
17573→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬¬⋀𝜑𝜓¬¬𝜓Modus ponens 17571, 17572
17574→𝜑→¬¬⋀𝜑𝜓¬¬𝜓Modus ponens 17531, 17573
17575→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬𝜓] into ax-3
17576→→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓Subs [𝜑↗→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17577→𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓Modus ponens 17575, 17576
17578→→𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓→→𝜑→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬⋀𝜑𝜓Subs [𝜓↗→¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗→¬𝜓¬⋀𝜑𝜓] into ax-2
17579→→𝜑→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬⋀𝜑𝜓Modus ponens 17577, 17578
17580→𝜑→¬𝜓¬⋀𝜑𝜓Modus ponens 17574, 17579
17581→→¬⋀𝜑𝜓¬𝜓→→¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬𝜓Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬𝜓] into impbi
17582→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓Subs [𝜑↗→¬𝜓¬⋀𝜑𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1
17583→→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓Subs [𝜑↗→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17584→𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓Modus ponens 17582, 17583
17585→→𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→𝜑→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓Subs [𝜓↗→¬𝜓¬⋀𝜑𝜓, 𝜒↗→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓] into ax-2
17586→→𝜑→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓Modus ponens 17584, 17585
17587→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓Modus ponens 17580, 17586
17588→→→¬⋀𝜑𝜓¬𝜓→→¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬𝜓¬⋀𝜑𝜓, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2
17589→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓Modus ponens 17581, 17588
17590→→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17591→𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓Modus ponens 17589, 17590
17592→→𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓Subs [𝜓↗→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜒↗→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓] into ax-2
17593→→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓Modus ponens 17591, 17592
17594→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓Modus ponens 17587, 17593
17595→→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓] into id
17596→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17597→→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1
17598→→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓Modus ponens 17596, 17597
17599→→→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑→¬⋀𝜑𝜓¬𝜓] into ax-2
17600→→→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓Modus ponens 17598, 17599
17601→→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Subs [𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2
17602→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17594, 17601
17603→→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1
17604→→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17602, 17603
17605→→→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→𝜑→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2
17606→→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17604, 17605
17607→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17596, 17606
17608→→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17609→𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17607, 17608
17610→→𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Subs [𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2
17611→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17609, 17610
17612→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17568, 17611
17613→→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Subs [𝜓↗𝜑, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2
17614→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17612, 17613
17615→→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Subs [𝜑↗→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17616→𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17614, 17615
17617→→𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2
17618→→𝜑→𝜑𝜑→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens 17616, 17617
17619→𝜑↔¬⋀𝜑𝜓¬𝜓Modus ponens id, 17614
17620↔→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓Subs [𝜓↗¬⋀𝜑𝜓, 𝜒↗¬𝜓] into pm5.32
17621→↔→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓→→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓Subs [𝜑↗→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓] into biimp
17622→→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓Modus ponens 17620, 17621
17623↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓Modus ponens 17619, 17622annotanannot
17624→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓Subs [𝜑↗⋀𝜑𝜓] into biimp
17625→→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓→𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓Subs [𝜑↗→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
17626→𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓Modus ponens 17624, 17625
17627→→𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓→→𝜑↔⋀𝜑𝜓𝜓→𝜑→⋀𝜑𝜓𝜓Subs [𝜓↗↔⋀𝜑𝜓𝜓, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
17628→→𝜑↔⋀𝜑𝜓𝜓→𝜑→⋀𝜑𝜓𝜓Modus ponens 17626, 17627
17629→𝜑→⋀𝜑𝜓𝜓Modus ponens 8176, 17628
17630→⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17631→→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗→⋀𝜑𝜓→𝜑⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
17632→⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 17630, 17631
17633→→⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2
17634→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓Modus ponens 17632, 17633
17635→→𝜑→⋀𝜑𝜓𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
17636→→→𝜑⋀𝜑𝜓→𝜑𝜓→⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
17637→⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓Modus ponens 6193, 17636
17638→→⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→𝜑𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17639→→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→𝜑𝜓Modus ponens 17637, 17638
17640→𝜑→⋀𝜑𝜓𝜑Subs [𝜓↗⋀𝜑𝜓] into ax-1
17641→→𝜑→⋀𝜑𝜓𝜑→𝜑→𝜑→⋀𝜑𝜓𝜑Subs [𝜑↗→𝜑→⋀𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1
17642→𝜑→𝜑→⋀𝜑𝜓𝜑Modus ponens 17640, 17641
17643→→𝜑→𝜑→⋀𝜑𝜓𝜑→→𝜑𝜑→𝜑→⋀𝜑𝜓𝜑Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
17644→→𝜑𝜑→𝜑→⋀𝜑𝜓𝜑Modus ponens 17642, 17643
17645→→⋀𝜑𝜓→𝜑𝜓→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
17646→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓Modus ponens pm3.4, 17645
17647→→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓→𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓Subs [𝜑↗→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
17648→𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓Modus ponens 17646, 17647
17649→→𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓→→𝜑→⋀𝜑𝜓𝜑→𝜑→⋀𝜑𝜓𝜓Subs [𝜓↗→⋀𝜑𝜓𝜑, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
17650→→𝜑→⋀𝜑𝜓𝜑→𝜑→⋀𝜑𝜓𝜓Modus ponens 17648, 17649
17651→→→𝜒𝜒→𝜓→𝜒𝜒→𝜑→→𝜒𝜒→𝜓→𝜒𝜒Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1
17652→𝜑→→𝜒𝜒→𝜓→𝜒𝜒Modus ponens 51, 17651
17653→→𝜑→→𝜒𝜒→𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→𝜓→𝜒𝜒Subs [𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2
17654→→𝜑→𝜒𝜒→𝜑→𝜓→𝜒𝜒Modus ponens 17652, 17653
17655→𝜑→𝜓→𝜒𝜒Modus ponens 815, 17654
17656→→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
17657→𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒Modus ponens 57, 17656
17658→→𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→𝜑→𝜓→𝜒𝜒→𝜑→→𝜓𝜒→𝜓𝜒Subs [𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2
17659→→𝜑→𝜓→𝜒𝜒→𝜑→→𝜓𝜒→𝜓𝜒Modus ponens 17657, 17658
17660→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗→𝜓𝜒] into ax-1
17661→→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓Subs [𝜑↗→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
17662→𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓Modus ponens 17660, 17661
17663→→𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜑→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓Subs [𝜓↗→⋀𝜑𝜓𝜓, 𝜒↗→→𝜓𝜒→⋀𝜑𝜓𝜓] into ax-2
17664→→𝜑→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓Modus ponens 17662, 17663
17665→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓Modus ponens 17629, 17664
17666→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜓] into imim2
17667→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1
17668→→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Modus ponens 17666, 17667
17669→→→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒] into ax-2
17670→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Modus ponens 17668, 17669
17671→→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17672→𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Modus ponens 17670, 17671
17673→→𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Subs [𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒] into ax-2
17674→→𝜑→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Modus ponens 17672, 17673
17675→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒Modus ponens 869, 17674
17676→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜓, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
17677→→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17678→𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17676, 17677
17679→→𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜓↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17680→→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17678, 17679
17681→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17675, 17680
17682→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜓, 𝜒↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17683→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17681, 17682
17684→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17665, 17683
17685→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into biimp
17686→→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓→𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓Subs [𝜑↗→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17687→𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓Modus ponens 17685, 17686
17688→→𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓→→𝜑↔𝜓⋀𝜑𝜓→𝜑→𝜓⋀𝜑𝜓Subs [𝜓↗↔𝜓⋀𝜑𝜓, 𝜒↗→𝜓⋀𝜑𝜓] into ax-2
17689→→𝜑↔𝜓⋀𝜑𝜓→𝜑→𝜓⋀𝜑𝜓Modus ponens 17687, 17688
17690→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒Subs [𝜑↗→𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
17691→→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒→𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒Subs [𝜑↗→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1
17692→𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒Modus ponens 17690, 17691
17693→→𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→⋀𝜑𝜓→𝜒𝜒Subs [𝜓↗→𝜒𝜒, 𝜒↗→⋀𝜑𝜓→𝜒𝜒] into ax-2
17694→→𝜑→𝜒𝜒→𝜑→⋀𝜑𝜓→𝜒𝜒Modus ponens 17692, 17693
17695→𝜑→⋀𝜑𝜓→𝜒𝜒Modus ponens 815, 17694
17696→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ax-2
17697→→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17698→𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17696, 17697
17699→→𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓→𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜓↗→⋀𝜑𝜓→𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17700→→𝜑→⋀𝜑𝜓→𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17698, 17699
17701→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17695, 17700
17702→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓Subs [𝜑↗→𝜓⋀𝜑𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
17703→→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓Subs [𝜑↗→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17704→𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓Modus ponens 17702, 17703
17705→→𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→𝜑→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓Subs [𝜓↗→𝜓⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓] into ax-2
17706→→𝜑→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓Modus ponens 17704, 17705
17707→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓Modus ponens pm3.2, 17706
17708→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into imim2
17709→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
17710→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Modus ponens 17708, 17709
17711→→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→→𝜓⋀𝜑𝜓→𝜓𝜒] into ax-2
17712→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Modus ponens 17710, 17711
17713→→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Subs [𝜑↗→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜓↗𝜑] into ax-1
17714→𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Modus ponens 17712, 17713
17715→→𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Subs [𝜓↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒] into ax-2
17716→→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Modus ponens 17714, 17715
17717→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒Modus ponens 17701, 17716
17718→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜓⋀𝜑𝜓, 𝜒↗→𝜓𝜒] into ax-2
17719→→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
17720→𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 17718, 17719
17721→→𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜓↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜒↗→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
17722→→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 17720, 17721
17723→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 17717, 17722
17724→→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
17725→→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 17723, 17724
17726→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into impbi
17727→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1
17728→→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜑↗→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
17729→𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 17727, 17728
17730→→𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
17731→→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 17729, 17730
17732→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒Modus ponens 4703, 17731
17733→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17734→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17726, 17733
17735→→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17736→𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17734, 17735
17737→→𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜓↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17738→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17736, 17737
17739→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17732, 17738
17740→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into id
17741→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17742→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1
17743→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17741, 17742
17744→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17745→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17743, 17744
17746→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17747→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17739, 17746
17748→→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1
17749→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17747, 17748
17750→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17751→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17749, 17750
17752→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17741, 17751
17753→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17754→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17752, 17753
17755→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17756→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17754, 17755
17757→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17684, 17756
17758→→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜓↗𝜑, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17759→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17757, 17758
17760→→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜑↗→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17761→𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17759, 17760
17762→→𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17763→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens 17761, 17762
17764→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒Modus ponens id, 17759
17765↔→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒Subs [𝜓↗→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into pm5.32
17766→↔→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒→→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒Subs [𝜑↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒] into biimp
17767→→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒Modus ponens 17765, 17766
17768↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒Modus ponens 17764, 17767pm5.33